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Events for September 2014 – January 2015

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Sep. 02, 2014 12:10pm (MATH …	Kempner Nandor Sieben (Northern Arizona University) X In the first part of the talk, we will recall the basic theory of impartial games. We�ll learn how to win at familiar games like NIM and precision bowling. Then, we�ll apply this knowledge to study games in which two players alternately pick elements of a given group until the picked elements generate the group. How to beat your neighbor at precision bowling and group generation
Sep. 02, 2014 3pm (Math 350)	Algebraic Geometry Agnes Beaudry (University of Chicago) X In the first talk, I will introduce some of the concepts which play a central role in homotopy theory. I will give an introduction to the concepts of stable homotopy groups, spectra, generalized cohomology theories and localization. I will also explain how formal group laws enter the subject. For the majority of the talk, I will only assume that the audience is comfortable with the concepts of topological spaces and their cohomology. The second talk will be focused on chromatic homotopy theory. The philosophy of chromatic homotopy theory is that the stable homotopy groups of the sphere $S$ can be re-assembled from the homotopy groups of a family of spectra $L_{n} S$ . Roughly, $L_{n} S$ is the $n$ -th chromatic layer of $S$ . Each layer corresponds to the height of a formal group law. The homotopy groups of the chromatic layers are related to the cohomology of the group of automorphisms of the corresponding formal group laws. In this talk, I will give an overview of this computational program. �I will also talk about the role played by elliptic curves and their deformation theory at chromatic level $2$ . I will assume that the audience has heard of spectral sequences. Chromatic homotopy theory
Sep. 03, 2014 4:05pm (MATH 3…	Grad Student Seminar Paul Lessard (CU-Boulder) X Eilenberg and Mac Lane developed or discovered category theory in the context of algebraic topology; the very utility of topological invariants such as homology, co-homology, and the homotopy groups is contingent on their functoriality. These particular invariants are moreover homotopy invariants. This property can be rephrased as those invariants factoring through the homotopy category, where homotopic maps are identified. We try and reverse this observation. Can we, starting with a functor, interpret it as a homotopy invariant by finding the right notion of homotopy? What data do we need to do so, and how universal are these constructions? In part one we will motivate and define Quillen's concept of a model category, and in part two we will outline how such a structure begets a homotopy category. From Invariants, to functors, to homotopy, to model categories, and back to homotopy: part 2
Sep. 09, 2014 11am (MATH 350)	Number Theory Alden Gassert (University of Colorado Boulder) X An iterated tower is a sequence of number fields that is generated by the iteration of a rational map defined over the base field. These dynamically generated number fields have received a growing attention over the past decade for a variety of reasons; in this talk I will discuss how these towers could lead to the first construction of infinite, yet finitely and tamely ramified, extensions. One way to ensure a successful construction is to find a tower in which the discriminants of the number fields does not grow too fast. I will demonstrate a method for how one might seek to study the growth of these number fields using the Chebyshev polynomials as an example. The iterated extensions arising from the Chebyshev polynomials are interesting in their own right. Arithmetic properties of iterated towers
Sep. 09, 2014 12:10pm (MATH …	Kempner Mati Rubin (Ben Gurion University) X A locally moving (LM) group for a regular topological space $X$ , is a group $G$ of homeomorphisms of $X$ which has the following property: For every nonempty open set $U$ , there is $g ∈ G$ such that: (1) $g$ is not the identity function, and (2) for every $x ∈ X ∖ U$ , $g(x) = x$ . A group $H$ is a locally moving (LM) group, if it is isomorphic to a group $G$ as above. Many groups of automorphisms of topological spaces, linear orderings, trees, Boolean algebras, measure algebras and some other types of structures are LM. Examples: (1) The group of all auto-homeomorphisms of a Euclidean space is LM. (2) The group of all $C∞$ homeomorphisms of a �� Euclidean space is LM. (3) The group of all automorphisms of the binary tree is LM. Using a certain theorem about LM groups, one can prove theorems of the following type: If $X$ and $Y$ are topological spaces such that $H(X)$ (= the group of all auto-homeomorphisms of $X$ ) is isomorphic to $H(Y)$ ,�� then�� $X$ is homeomorphic to $Y$ . Similar theorems for linear orderings, trees, Boolean algebras, measure algebras and some other types of structures are also true. A recent theorem states that: The first order theory of every locally moving group is undecidable. (This solves in much more generality a question of Mark Sapir about the R. Thompson groups). I shall state and explain that "certain theorem" mentioned above. Then I'll speak about consequences of that theorem including the undecidability theorem. If time allows, I shall mention some open problems. Locally moving groups, reconstruction and undecidability
Sep. 09, 2014 2pm (MATH 350)	Lie Theory Erica Shannon (CU) X Given a parabolic subgroup of a Coxeter group, we may hope to describe a set of nice coset representatives for this subgroup. Deodhar's Lemma shows us how to directly compute a set of coset representatives with the property that every prefix of a coset representative is also on the list. Time permitting, we'll discuss an application of Deodhar's Lemma to the 56-dimensional minuscule module for the simple Lie algebra of type E7. No previous knowledge of Coxeter groups will be assumed. Deodhar's Lemma and an Application to Representation Theory
Sep. 09, 2014 3pm (Math 350)	Algebraic Geometry Elizabeth Gillaspy (University of Colorado) X The goal of this talk is to explain my thesis research and why we care. In the first part of the talk, I will define the objects in the title and explain how the K-theory of groupoid C-algebras can tell us about other mathematical objects, from dynamical systems to string theory. My hope is that this will be a gentle introduction to the topic(s) at hand; no prior familiarity with groupoids or with C-algebras will be assumed. In the second part of the talk, I'll discuss the particular question I've investigated about the K-theory of twisted groupoid C-algebras, why I chose it, and the progress that I've made so far. Time permitting, I will sketch some of the proofs, so this part of the talk will be more technical than the first part. K-theory for twisted groupoid C-algebras
Sep. 09, 2014 11pm (Math 220)	Noncomm Geometry Alexander Gorokhovsky Introduction to cyclic (co)homology.
Sep. 10, 2014 4:05pm (MATH 3…	Grad Student Seminar John Willis (CU-Boulder) X Schemes are objects central to the study of algebraic geometry, but what are they? A scheme is a locally ringed space that admits an open cover by affine schemes, sure, but what is a locally ringed space? What is an affine scheme? I will try to answer these questions by motivating the definition of a scheme with basic real and complex analysis. The basic yoga is that schemes are weird, because commutative rings are weird; any non-abelian category is weird. But Riemann Surfaces are not weird at all, and much intuition for how schemes behave, and what sorts of things should be true about them, can be obtained through the lens of complex geometry where one has holomorphic structure to work with - contractible neighborhoods, differentiability, and other such familiar and friendly notions. Once we have drawn some pictures and seen, at least heuristically, why we should think of commutative rings as the natural dwelling place for functions, we will define abstractly what a scheme is and give some examples. What Is a Scheme?
Sep. 11, 2014 3pm (Webber 20…	Algebraic Geometry Chris Ormerod (Cal Tech) X There are many integrable ordinary differential equations that may be derived as isomonodromic deformations. Symplectic geometry gives us insight into how such system possesses a Hamiltonian description. Analogously, there are many integrable ordinary difference equations that are derived as discrete isomonodromic deformations and connection preserving deformations. By considering a geometric setting for differential and difference Lax pairs, we present some preliminary work that suggests the evolution of these systems possesses an analogous description. The geometry of discrete isomonodromy
Sep. 16, 2014 2pm (Math 220)	Functional Analysis Judith Packer (University of Colorado, Boulder) X We continue our discussion introducing groupoids. All are welcome. Introduction to Groupoids part 2 Sponsored by the Meyer Fund
Sep. 16, 2014 2pm (MATH 350)	Lie Theory Megan Ly (CU) X The Huneke-Wiegand conjecture, a long-standing open problem in commutative algebra has prompted much recent study.� In the category of numerical monoid algebras, Garcia-Sanchez and Leamer provide a reduction theory that equates the Huneeke-Wiegand conjecture to finding certain irreducible arithmetic sequences within numerical monoids.� This talk focuses on Leamer monoids, whose elements correspond to arithmetic sequences of a given step size within a fixed numerical monoid, and its factorization theory.� In this talk we will provide a description for the first element $x0$ in the Leamer monoid for numerical monoids generated by two integers using Apery sets.� We apply our results to prove the Huneke-Wiegand Conjecture for all numerical monoid algebras of two generators and provide direction for potentially proving the conjecture for numerical monoid algebras with more generators. The Factorization Theory of Leamer Monoids
Sep. 16, 2014 11pm (Math 220)	Noncomm Geometry Alexander Gorokhovsky Introduction to cyclic (co)homology (contd.)
Sep. 18, 2014 3pm (Weber 201…	Algebraic Geometry Sofia Tirabassi (University of Utah) X We give a complete classification of varieties of maximal Albanese dimension . chi equal to 1 and irregularity 2dimX-1. This is a joint work with Z. Jiang and M. Lahoz. Varieties with Chi equal to 1
Sep. 23, 2014 11am (MATH 350)	Number Theory William Chen (Macquarie University) X The birth of geometric discrepancy theory is usually attributed to the fundamental work of Klaus Roth in 1954. The present scope of the subject is due in no small part to the many important results of Wolfgang Schmidt in the 1960s and 1970s. It is fair to say that every subsequent worker in the subject have been motivated and encouraged, directly or indirectly, by these two pioneers and their work. Lower bound results in discrepancy theory exhibit the limitations to just point distributions, whereas upper bound results lead to point distributions that are close to best possible under such limitations. In this expository talk, we shall discuss some of the main results obtained over the last 60 years, and introduce to the audience a number of lower and upper bound techniques. We shall also briefly discuss some open questions. A quick tour of discrepancy theory
Sep. 23, 2014 12:10pm (MATH …	Kempner Gerard Misiolek (Notre Dame) X I will describe some recent results on local ill-posedness (in the sense of Hadamard) of the Cauchy problem for the incompressible Euler equations of hydrodynamics. Ill-posedness of the incompressible Euler equations in borderline spaces
Sep. 23, 2014 2pm (Math 220)	Functional Analysis Judith Packer (Department of Mathematics, CU Boulder) X We continue our introductory lectures on groupoids. In this lecture, we will introduce left Haar systems, and hopefully will discuss C*-algebras associated to locally compact groupoids having a left Haar system. Introduction to Groupoids, Part 3 Sponsored by the Meyer Fund
Sep. 23, 2014 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X In this series of two talks, the goal is to study combinatorial realizations of representations induced from unipotent subgroups. The first talk will build a combinatorial framework for the representations of the finite general linear groups via symmetric functions. The goal is to have a setting where representations have a pleasing combinatorial existence even without knowing the algebraic underpinnings. The second talk will then find the induced characters of unipotent groups in this combinatorial setting. This is joint work with S. Andrews. The combinatorial representation theory of the finite general linear groups
Sep. 23, 2014 11pm (Math 220)	Noncomm Geometry Alexander Gorokhovsky Introduction to cyclic (co)homology (contd.)
Sep. 24, 2014 4:05pm (MATH 3…	Grad Student Seminar Shawn Burkett (CU-Boulder) X Algebraic group theory is, essentially, the intersection of algebraic geometry and group theory. Algebraic geometry, in a classical sense, is the study of algebraic sets (the vanishing loci of systems of polynomials) in affine or projective space. An algebraic group is an abstract group which is also an algebraic set, where the group operations are given by polynomial functions. Among the most widely studied are the affine algebraic groups, those which may be embedded in GL(V), the automorphism group of some (finite dimensional) vector space V. After defining affine algebraic groups, we will discuss some of the important subgroups which, in many ways, control the structure of the groups. Time permitting, we will discuss finite groups of Lie type, which are rational points of a particular type of linear algebraic group. An Introduction to Algebraic Groups
Sep. 25, 2014 3pm (Weber 201…	Algebraic Geometry Mark Shoemaker (University of Utah) X Mirror symmetry is the name given to a broad collection of mathematical conjectures arising from a type of duality in physics. Roughly it states that certain information about a smooth variety M should by expressible in terms of different properties of a ``mirror manifold�� W. Rephrasing questions about M in terms of W has led to striking solutions to many previously intractable problems in geometry. In this talk I will give a friendly introduction to the mathematics of mirror symmetry, and outline some ways in which given a manifold M one can construct its mirror W. Not all of these constructions agree however, and sometimes one is left with different spaces which should be mirror to the same M. This ``multiple mirror�� phenomenon has interesting mathematical implications. In particular I will show that in certain settings, the mirror manifolds which arise are in fact birational to one another. An introduction to mirror symmetry and the question of multiple mirrors
Sep. 25, 2014 4pm (Weber 201…	Algebraic Geometry Olivia Dumitrescu (Hanover Universitaat) X In the first part of the talk I will discuss the Eynard-Orantin theory to the family of spectral curves of Hitchin fibrations over a smooth base curve C of genus at least 2. In particular, we study rank 2 holomorphic Higgs field and we identify the spectral curve of the Eynard-Orantin as the spectral curve of Hitchin fibration. In the second part we generalize this construction to meromorphic Higgs fields with possibly singular spectral curve in the compactified cotangent bundle. We identify the spectral curve of the Eynard-Orantin recursion with a divisor in a ruled surface over the curve C. We further apply recursion to quantize spectral curve. We present as simple examples of our theory meromorphic Higgs bundles over the rational curve, and we obtain well-known classical equations as Airy function and Catalan recursion. This talk is based on my joint work with Motohico Mulase, U.C. Davis. Quantization of singular spectral curves for meromorphic Higgs bundles of rank 2
Sep. 26, 2014 4:15pm (MATH 3…	Probability Carl Mueller (U. Rochester) Hitting questions and multiple points for stochastic PDE (SPDE) in the critical case
Sep. 30, 2014 2pm (Math 220)	Functional Analysis Judith Packer (University of Colorado) X We continue our discussion of r-discrete groupoids with left Haar systems and the C*-algebras that arise from them. Introduction to Groupoids, part 4 Sponsored by the Meyer Fund
Sep. 30, 2014 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X In this series of two talks, the goal is to study combinatorial realizations of representations induced from unipotent subgroups.� The first talk will build a combinatorial framework for the representations of the finite general linear groups via symmetric functions.� The goal is to have a setting where representations have a pleasing combinatorial existence even without knowing the algebraic underpinnings.� The second talk will then find the induced characters of unipotent groups in this combinatorial setting.� This is joint work with S. Andrews. Supercharacters and the generalized Gelfand--Graev representations
Sep. 30, 2014 3pm (Math 350)	Algebraic Geometry Matthew Grimes (University of Colorado) X Recent work on the log minimal model program for the moduli space of curves, as well as past results of Caporaso, Pandharipande, and Simpson motivate an investigation of compactifications of the universal moduli space of slope semi-stable vector bundles over moduli spaces of curves arising in the Hassett-Keel program.� Our main result is the construction of a universal moduli space of slope semi-stable sheaves which compactifies the moduli space of vector bundles over the moduli space of pseudo-stable curves. The first half of the talk will emphasize accessibility and focus on background material: geometric invariant theory, moduli problems, and the log-minimal model program.� In the second segment, we will discuss the construction of the universal moduli space of vector bundles. Universal moduli spaces of vector bundles and the log minimal model program on the moduli of curves
Sep. 30, 2014 11pm (Math 220)	Noncomm Geometry Alexander Gorokhovsky Introduction to cyclic (co)homology (contd.)
Oct. 01, 2014 4pm (MATH 350)	Grad Student Seminar Shawn Burkett X Algebraic group theory is, essentially, the intersection of algebraic geometry and group theory. Algebraic geometry, in a classical sense, is the study of algebraic sets (the vanishing loci of systems of polynomials) in affine or projective space. An algebraic group is an abstract group which is also an algebraic set, where the group operations are given by polynomial functions. Among the most widely studied are the affine algebraic groups, those which may be embedded in GL(V), the automorphism group of some (finite dimensional) vector space V. After defining affine algebraic groups, we will discuss some of the important subgroups which, in many ways, control the structure of the groups. Time permitting, we will discuss finite groups of Lie type, which are rational points of a particular type of linear algebraic group. An Introduction to Algebraic Groups: Part 2
Oct. 02, 2014 3pm (Webber 20…	Algebraic Geometry Dmitry Korotkin (Concordia University, Montreal) X Isomonodromic tau-functions corresponding to various special matrix Riemann-Hilbert problems turn out to be meromorphic sections of certain line bundles (as a rule of Hodge determinant line bundle) over underlying moduli spaces. This allows to use them to obtain (both new and old) relations between divisor classes on these moduli spaces (spaces of admissible covers, moduli spaces of holomorphic differentials on Riemann surfaces etc). We review these and other applications of such objects in the theory of random matrices, spectral geometry and Frobenius manifolds. The talk is based on joint works with A.Kokotov and P.Zograf. Isomonodromic tau-functions and sections of Hodge line bundle over moduli spaces.
Oct. 07, 2014 12:10pm (MATH …	Kempner Claire Levaillant (UC Santa Barbara) X Classical computers function with bits that are 0� and 1. Instead quantum computers function with states that� are complex linear combinations of� quantum bits \|0> and \|1>. In this talk we will give an� overview of how to make quantum gates, that is how to� mathematically and physically realize the unitary� transformations that make a state evolve to another state. Our approach is based on the pioneering work of Michael� Freedman, Chetan Nayak and Sankar Das Sarma among others in� topological quantum computation. An important physical� operation consists of braiding quasi-particles which are� named anyons. �Making a braid on anyons consists of interchanging their� positions. The mathematical theory which we use behind the� physics of braiding anyons is the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. We will introduce this� theory and show how to make some of the quantum gates that� make quantum computation universal, that is, it is possible� with these very few gates to obtain good approximations� to any desired gate. Recent developments in universal quantum� computation
Oct. 07, 2014 2pm (Math 220)	Functional Analysis Arlan Ramsay (University of Colorado, Boulder) X The speaker will discuss the tangent groupoid, an important groupoid that appears in geometry and analysis. The tangent groupoid Sponsored by the Meyer Fund
Oct. 07, 2014 2pm (MATH 350)	Lie Theory Cliff Blakestad (CU) X The Weil Conjectures (now theorems) suggest deep connections between counting solutions to equations over finite fields and the topology of the complex solutions to those same equations. We will explore how one can use these connections to apply topological information about complex spaces toward answering counting questions related to finite fields and see some of the challenges involved in this approach. Counting with Topology
Oct. 07, 2014 11pm (Math 220)	Noncomm Geometry Joseph Migler Introduction to K-theory and K-homology
Oct. 08, 2014 4pm (MATH 350)	Grad Student Seminar Megan Ly (CU-Boulder) X Numerical monoids, which are co-finite additive submonoids of the natural numbers have long been studied for their non-unique factorization properties. This talk will focus on two of these properties: elasticity and omega-primality. The elasticity of an element is a coarse measure of how different the lengths of its factorizations can be. We study the set of elasticities for a class of numerical monoids and find its formula. Next we study the omega-primality function, which measures how far an element is from being prime. We analyze the omega-primality to provide a closed form for portions of the function. This talk assumes no background knowledge of monoids so undergraduates are encouraged to attend!!! An Introduction to Numerical Monoids
Oct. 09, 2014 3pm (Weber 201…	Algebraic Geometry Dhruv Ranganathan (Yale) X In the first part of my talk, I will introduce various flavours of tropicalization, a process that associates piecewise-linear polyhedral objects to algebraic varieties. I will explain how this piecewise linear geometry ties intimately to degeneration and compactification of (families of) algebraic varieties. Nonarchimedean analytic geometry, in the sense of Berkovich, provides an elegant and powerful framework in which to study these so-called skeletons. In the second part of my talk we will explore the applications of tropicalization, as a degeneration technique, to computing enumerative invariants. I will focus on the case of target curves, where insights from the theory of Berkovich spaces have begun to dissolve some of the mystery behind the success of these combinatorial techniques. For instance, the relationship between the analytification of Hurwitz space and its skeleton precisely explains how and why tropical geometry can be used to compute enumerative invariants of target curves. Tropicalization and nonarchimedean enumerative geometry
Oct. 09, 2014 3pm (MATH 350)	Probability Michael Damron (Indiana University) X For a sub-additive ergodic sequence {X_{m,n}}, Kingman's theorem gives convergence for the terms X_{0,n}/n to some non-random number g. In this talk, I will discuss the convergence rate of the mean EX_{0,n}/n to g. This rate turns out to be related to the size of the random fluctuations of X_{0,n}; that is, the variance of X_{0,n}, and the main theorems I will present give a lower bound on the convergence rate in terms of a variance exponent (if it exists). The main assumptions are that the sequence is not diffusive (the variance does not grow linearly) and that it has a weak dependence structure. Various examples, including first and last passage percolation, bin packing, and longest common subsequence fall into this class. This is joint work with Tuca Auffinger and Jack Hanson. Rate of convergence of the mean for sub-additive ergodic sequences
Oct. 14, 2014 2pm (MATH 350)	Lie Theory Jon Kujawa (University of Oklahoma) X For more than a century Schur-Weyl duality has proven to be a powerful and popular tool in representation theory. It relates the representations of GL(n) and the symmetric group on r letters and allows you to pass information between these two Type A groups. In a classic paper in the early 90's Beilinson, Lusztig, and MacPherson gave us a geometric way to construct and think about Schur-Weyl duality. In joint work with Bao, Li, and Wang we worked out the analogue in types B and C. In particular, we naturally realize the hyperoctahedral Schur algebra studied by Green. My goal is to give an accessible overview of the construction suitable for a general audience. Geometric Schur-Weyl Duality Sponsored by the Meyer Fund
Oct. 14, 2014 11pm (Math 220)	Noncomm Geometry Joseph Migler Introduction to K-theory and K-homology (continued).
Oct. 21, 2014 2pm (Math 220)	Functional Analysis Elizabeth Gillaspy X In preparation for Alex Kumjian's lecture next week, I will discuss how we can associate a C-algebra to a directed graph. There are two approaches -- one using generators and relations, and one using groupoids -- that yield isomorphic C-algebras. The (groupoid) C*-algebra of a directed graph Sponsored by the Meyer Fund
Oct. 21, 2014 2pm (MATH 350)	Lie Theory Matthew Tai (University of Pennsylvania) X For certain representations V of certain groups G, we can define a notion of G-harmonic polynomials on V in the sense of Kostant and Chevalley.� I will describe a construction of Kirillov's aimed at computing these polynomials when G is a compact Lie group and also talk about connections to matrix algebras over noncommutative bases. Intro to Family Algebras Sponsored by the Meyer Fund
Oct. 21, 2014 3pm (Math 350)	Algebraic Geometry Samouil Molcho (University of Colorado) X Higher Dimensional Analogues of Stable Maps. In this talk I will discuss stable maps X-->V where the source X may not be a curve but rather a higher dimensional variety. Specifically, suppose V is a toric variety and H a subtorus of its torus. I will discuss Alexeev's moduli space A(V) of H-equivariant maps X-->V, where the source is a broken toric variety with torus H, and its analogue K(V) where X and V are equipped with logarithmic structures. I will then give an explicit combinatorial description of K(V) as a toric stack. When the dimension of H is 1, this description reduces to the description of the stack of genus 0 logarithmic stable maps of Gross-Siebert. In the first half of the talk I will give a brief introduction to the ideas and results we need from logarithmic and toric geometry, and discuss how logarithmic geometry appears when studying compactifications of moduli spaces. Higher dimensional analogues of stable maps
Oct. 21, 2014 11pm (Math 220)	Noncomm Geometry Joseph Migler Introduction to K-theory and K-homology (continued).
Oct. 22, 2014 4pm (MATH 350)	Grad Student Seminar Pearce Washabaugh (CU-Boulder) X One naturally expects spaces with the same geometry to propagate waves in a similar fashion. However, whether the converse is true or not is far from obvious. If we know how a space vibrates (i.e. listen to the sound it makes) can we determine the underlying geometry of the space? The answer requires a surprising breadth of mathematics, from Riemannian geometry to Galois theory. Hearing the Shape of a Drum
Oct. 23, 2014 3pm (MATH 350)	Probability Antonio (Tuca) Auffinger (Northwestern) X Spin glasses are magnetic systems exhibiting both quenched disorder and frustration, and have often been cited as examples of "complex systems." As mathematical objects, they provide several fascinating structures and conjectures. This talk will cover recent progress that shed more light in the mysterious and beautiful solution proposed 30 years ago by G. Parisi. We will focus on properties of the functional order parameter of the famous Sherrington-Kirkpatrick model and we will explain a proof of uniqueness of the Parisi functional. Based on joint works with Wei-Kuo Chen. Strict convexity of the Parisi functional
Oct. 23, 2014 3pm (Weber 201…	Algebraic Geometry Mark Walsh (Wichita State University) X The moduli space of positive scalar curvature metrics A central theme in modern geometry is the relationship between curvature and topology. Given a smooth manifold, we may ask whether it admits a geometric structure (Riemannian metric) which satisfies particular curvature constraints, say positive, constant or negative curvature. For example, we know that the 2-torus admits a constant zero-curvature geometry but cannot admit everywhere positive (or negative) curvature, whereas the 2-sphere admits positive curvature geometries but not flat or negative curvature ones. A particular case of this problem, for which much is known, is the question of whether or not a smooth manifold admits metrics whose scalar curvature is strictly positive. Moreover, given a manifold which admits such metrics, we may wonder about the topology of the space of such metrics, or its corresponding moduli spaces. Are these spaces path connected? Do they have non-trivial homotopy or homology? The first of my two talks will be a gentle introduction to the existence problem for positive scalar curvature metrics, beginning with the classical case in dimension 2. I will go on in the second talk, to discuss recent progress in understanding the topology of the space of positive scalar curvature metrics, with a particular emphasis on the moduli space obtained by the action of the automorphism group of the manifold. The moduli space of positive scalar curvature metrics
Oct. 24, 2014 3pm (ECCR 245)	Kempner James O. Ramsay (McGill University Department of Psychology) X This will be a Joint Mathematics & Applied Mathematics Colloquium.� Note the unusual time and place. Principal components analysis is an invaluable tool in multivariate or functional data analy- sis, but it suffers from several defects. All fits are required to be by least squares, there is no distinction made between principal component vectors/functions and principal component scores as parameters, eigenvectors/functions as objects spanning the subspace are accorded a interpretive or substantive significance that they dont deserve, and it is difficult to introduce estimation strategies now considered essential with other methods such as regularization. This new approach is based on a parameter cascade that defines factor scores as smooth functions of principal component vectors/functions. In the functional case, registration of time warping parameters are in turn defined as functions of factor scores and hence indirectly of principal components. In this approach, any suitable loss function may be employed for any variable in the multivariate case, or vary over time in the functional case. The method is also adaptable to non-flat manifold estimation. Multivariate and functional principal components without eigenanalysis
Oct. 28, 2014 11am (MATH 350)	PDE/Analysis Magdalena Czubak (SUNY Binghamton) X We review Liouville theorems for the Navier-Stokes equation on the Euclidean space. In particular, the problem for the stationary Navier-Stokes equation in 3D under finite Dirichlet norm is open. In this talk we answer the analogous question on the 3D hyperbolic space. This is joint work with Chi Hin Chan. Liouville theorems for the Navier-Stokes equation on the hyperbolic space Sponsored by the Meyer Fund
Oct. 28, 2014 11am (MATH 350)	Number Theory Valentijn Karemaker (Utrecht University) X Let G denote a linear algebraic group over Q and K and L two number fields. Assume that there is a group isomorphism of points on G over the adeles of K and L, respectively. We establish conditions on the group G, related to the structure of its Borel groups, under which K and L have isomorphic adele rings. Under these conditions, if K or L is a Galois extension of Q and G(A_K) and G(A_L) are isomorphic, then K and L are isomorphic as fields. As a corollary, we show that an isomorphism of Hecke algebras for GL(n) (for fixed n > 1), which is an isometry in the L^1 norm over two number fields K and L that are Galois over Q, implies that the fields K and L are isomorphic. This can be viewed as an analogue in the theory of automorphic representations of the theorem of Neukirch that the absolute Galois group of a number field determines the field if it is Galois over Q. Hecke algebra isomorphisms and adelic points on algebraic groups
Oct. 28, 2014 12:10pm (MATH …	Kempner Daniel Stroock (MIT) X More or less at the same time, in 1896 Hadamard and de la Vall ?ee proved that lim ?(n)logn=1 n?? n where ?(n) denotes the number of prime numbers p ? n, a famous result known as the prime number theorem. Their proofs were magnificent examples of the power of analytic function theory to solve problems in number theory, and to understand their proofs one has to have the mastery of complex analysis that they had. Over the course of time, their proofs were simplified and other proofs were given. However, the first proof that could be called �elementary� was given by D.J. Newman in a MAA article that appeared in 1980. Newman�s proof requires only that one know that the Riemann zeta function has no zeroes in the half space {z ? C : R(z) ? 1}, and the way that he gets away with so little information is that he applies a novel Tauberian theorem, one that he invented himself. Newmans argument was further refined by D. Zagier on the 100th birthday of the prime number theory, and it Zagier�s article on which my lecture is based. Unfortunately, elementary as Newman�s proof is, it cannot be given in 40 minutes. Thus, in this lecture, I will concentrate on his Tauberian theorem and will only sketch the rest of the argument. The prime number theorem
Oct. 28, 2014 2pm (MATH 350)	Lie Theory Amanda Schaeffer Fry (Metro State) X The so-called �local-global� conjectures in the representation theory of finite groups relate the representation theory of G to that of certain proper subgroups, such as Sylow normalizers. Since the relationship often involves comparing the number of representations satisfying certain properties, many of these are nicknamed �counting conjectures�. I will introduce some of the conjectures and discuss recent results (by many authors) regarding them. Some �Counting� Conjectures in the Representation Theory of Finite Groups Sponsored by the Meyer Fund
Oct. 28, 2014 2pm (Math 220)	Functional Analysis Elizabeth Gillaspy X In this talk I will sketch a proof of the isomorphism between the universal C-algebra and the groupoid C-algebra associated to a directed graph E. Time permitting, I will also discuss more examples of graph C-algebras. Graph C-algebras, part 2 Sponsored by the Meyer Fund
Oct. 28, 2014 11pm (Math 220)	Noncomm Geometry Alex Nita Fredholm Modules
Oct. 30, 2014 3pm (Weber 201…	Algebraic Geometry Lalit Jain (University of Wisconsin) X The monodromy of a family of varieties is a measure of how homology classes vary. Surprisingly, many familiar ideas in number theory, such as Galois representations and Cohen-Lenstra heuristics, are closely linked to monodromy of specific families. In this talk I will define monodromy, and describe original work of computing monodromy for moduli spaces of covers of the projective line (Hurwitz spaces). This work generalizes previous results of Achter-Pries, Yu and Hall on hyperelliptic families. Only basic knowledge of algebraic topology and number theory is required. Monodromy computations in topology and geometry
Oct. 31, 2014 4pm (Math 350)	Functional Analysis Alex Kumjian (University of Nevada - Reno) Higher rank graphs, groupoids and C*-algebras Sponsored by the Meyer Fund
Nov. 04, 2014 11am (MATH 350)	Number Theory Caleb Shor (Western New England University) X Given an algebraic curve C of genus g, we say a point P is a Weierstrass point if dim(L(gP))>1, where L(D) is the Riemann-Roch space associated to a divisor D.� One can generalize this to define a higher-order Weierstrass point, and one can also talk about the weight of a Weierstrass point. In this talk, we will consider Weierstrass points on superelliptic curves, which are curves of the form y^n=f(x) for f(x) a polynomial of degree d.� Under a mild hypothesis, it is well known that the branch points of such curves are Weierstrass points.� We will investigate the weights of these branch points for given values of n and d and use them to obtain some asymptotic results.� We will also look at the various weight distributions that can arise on certain families of hyperelliptic curves of low genus and prescribed automorphism groups. Ordinary and higher-order Weierstrass points on cyclic covers of the projective line
Nov. 04, 2014 3pm (Math 350)	Algebraic Geometry P�l Zs�mboki (University of Washington) X Starting with linear endomorphisms of a 2-dimensional complex vector space, and moving on to line bundles on a real conic, I will discuss how the problem of finding a moduli space can involve having to extend our notion of geometrical space. After that, I will talk about how a choice of a meaningful compactification of the moduli space of vector bundles on a surface has led to the proof of irreducibility of said moduli space. Introduction to moduli spaces and compactification Sponsored by the Meyer Fund
Nov. 04, 2014 4pm (Math 350)	Algebraic Geometry P�l Zs�mboki (University of Washington) X I will discuss an approach to getting a meaningful boundary to the moduli space of G-bundles on a smooth, proper scheme using derived objects. Homotopical Algebraic Geometry will arise as the natural framework to treat this problem in. No knowledge of higher stacks will be assumed. Towards the compactification of the moduli space G-torsors via perfect Lie algebra complexes Sponsored by the Meyer Fund
Nov. 04, 2014 11pm (Math 220)	Noncomm Geometry Rapha�l Ponge (Seoul National University) X This will be report on a series of joint papers with Hang Wang (U. Adelaide, Australia). The general aim of these papers is to use tools from noncommutative geometry to study conformal geometry and some noncommutative incarnations of conformal geometry. In this talk, I will present two main results. The first main result is a reformulation of the local index formula in the setting of conformal-diffeomorphism invariant geometry. The second main result is the construction of a new family of global conformal invariants taking into account the action of the group of conformal-diffeomorphisms. These invariants are not of the same type as the conformal invariants considered by Spyros Alexakis in his celebrated solution of the Deser-Schwimmer. The arguments leading to both results heavily rely on noncommutative geometry. In particular, a crucial use is made of the conformal invariance of the Connes-Chern character. However, the main results are ultimately stated in differential-geometric fashion. Noncommutative geometry and conformal geometry: local index formula and conformal invariants.
Nov. 05, 2014 4pm (MATH 350)	Grad Student Seminar Jonathan Lamar X Line up a deck of cards on a table and repeatedly switch pairs of them at random. One might ask how many switches are necessary and/or sufficient to produce a deck which is well-shuffled. Answering this question and others like it motivates the study of random walks on groups, which has surprising connections to representation theory. I will provide a gentle introduction to this subject. If time permits, I will also discuss the result of Diaconis and Shahshahani (1981) that for the above shuffling process on an n card deck, a rapid shift from low to high entropy occurs after about (n/2)*log(n) switches. From Card Shuffling to Representation Theory and Back
Nov. 06, 2014 3pm (Weber 201…	Algebraic Geometry Melody Chan (Harvard) X The genus of Brill-Noether curves I'll discuss an ongoing joint project with Lopez, Pflueger, and Teixidor, in which we use a surprising theorem on random standard Young tableaux to give a new proof, using degenerations and limit-linear series, of the classical formula of Eisenbud-Harris and Pirola for the genus of the Brill-Noether curve. No background will be assumed. Topology of tropical moduli spaces The moduli space of n-marked, genus g tropical curves is a cell complex that was identified in work of Abramovich-Caporaso-Payne with the boundary complex of the complex moduli space M_{g,n}. I will report on new results on the topology of tropical M_{1,n} and M_{2,n}, obtaining as corollaries new calculations of the top-weight cohomology of the complex moduli spaces M_{1,n} and M_{2,n}. Joint work, in part, with Galatius and Payne. The genus of Brill-Noether curves
Nov. 11, 2014 11am (MATH 350)	Number Theory Leonhard Summerer (University of Vienna) X In this talk I want to introduce a method based on the geometry of numbers and in particular on the study of the successive minima functions with respect to a certain lattice and a suitable one-parameter family of convex bodies. This approach leads to the definition of some new approximation constants and in turn to some new transference inequalities. The related geometric picture in conjunction with some recent results of D. Roy motivates some best possible bounds in the case of simultaneous approximation of several real numbers. Geometry of Numbers and simultaneous Approximation
Nov. 11, 2014 12:10pm (MATH …	Kempner Anca Radulescu (SUNY New Paltz) X The behavior of orbits for iterated logistic maps has been widely studied since the dawn of discrete dynamics as a research field. Existing results refer not only to the family of real polynomials $f : ℝ \to ℝ$ , $fμ(x) =μ x(1-x)$ , for $μ >0$ , but also to the context of complex maps $f : ℂ \to ℂ$ , parametrized as $fc(z)=z2+c$ , with $c ∈ C$ . However, little is is known about orbit behavior if the map changes along with the iterations. \\ \noindent We investigate how the theory changes if the dynamical scheme involves two functions, $f0$ and $f1$ , iterated according to a prescribed binary sequence of $0$ s and $1$ s. In particular, we observe the effects of the structure of the symbolic sequence (periodicity, complexity, etc) on the complexity of the resulting system and (visually) on the topological structure of its Julia set.\\ \noindent This direction is of potential interest to a variety of applications (including genetic and neural coding), since it investigates how an occasional or a reoccurring error in a replication or learning algorithm may affect the outcome. Real and complex dynamics for symbolic sequences of logistic maps
Nov. 11, 2014 2pm (MATH 350)	Lie Theory Derek Wise (University of Erlangen) X While groups formalize the notion of symmetry, "2-groups" include also the idea that symmetries might be related to each other by symmetries of their own. I will explain 2-groups, which are categories equipped with a group-like multiplication, and discuss their representation theory. Just as groups have representations on vector spaces, 2-groups have representations on "2-vector spaces", which are categories analogous to vector spaces. For a simple reason that I will explain, the most interesting representations of Lie 2-groups are all infinite-dimensional. I will describe Lie 2-group representations on an appropriate kind of infinite-dimensional 2-vector space, and show that these can be nicely understood in terms of objects familiar from ordinary group representation theory and geometry. Higher Symmetry: Lie 2-Groups and their Representations Sponsored by the Meyer Fund
Nov. 11, 2014 11pm (Math 220)	Noncomm Geometry Josh Frinak X If $u:E0→ E1$ is morphism of complex vector bundles over a smooth manifold $M$ which is an isomorphism over a subset $A$ , then $u$ determines a class in the relative $K$ -group $K(M,A)$ . I intend to present Quillen's construction of the Chern character which involves the use of a $Z2$ -graded variant of the concept of a connection called a superconnection. Given a convenient choice of superconnection $𝔸$ we are interested in the curvature $θ=A2$ . It will turn out that the super trace of $e^{θ}$ will represent the Chern character, $ch E0-ch E1$ , in de Rham cohomology. Chern character via superconnections.
Nov. 13, 2014 3pm (Weber 201…	Algebraic Geometry Dmitry Zakharov (NYU) X Given an algebraic curve with marked points and integer weights on the markings, we can consider the corresponding divisor. This defines an Abel--Jacobi map from the moduli space of marked curves of compact type to the universal Jacobian variety. Pulling back relations from the universal Jacobian for various values of the weights gives a plethora of tautological relations on the space of curves of compact type. These relations include those discovered by Faber, Getzler, Belorousski and Pandharipande, and Tavakol, and this method was also used by Hain to compute the double ramification cycle. I will talk about the extension of the Abel--Jacobi map to a larger moduli space of marked curves, the corresponding extended formula for the double ramification cycle, and Pixton's conjectures about the extensions of these relations to the entire Deligne-Mumford compactification. The Abel--Jacobi map and relations in the tautological ring
Nov. 13, 2014 3pm (MATH 350)	Probability Douglas Rizzolo (U. Washington) X We will discuss the motion a tagged gas particle in a gravitational field. Our starting point will be a Markov approximation to a Lorentz gas model with variable density. We investigate how the density of the ambient gas impacts the recurrence or transience of the tagged particle and we will show that there are multiple scaling regimens leading to nontrivial diffusive limits. This talk is based on joint work with Krzysztof Burdzy. A gas particle in a gravitational field
Nov. 14, 2014 4pm (Math 350)	Functional Analysis Christopher Seaton (Rhodes College, Memphis, TN) X In many applications, one is interested in a topological groupoid whose object and arrow spaces are not smooth manifolds yet do come equipped with a natural notion of smoothness. Often, this notion of smoothness can be understood by giving each space the structure of a differentiable or differentiable stratified space. In this talk, we will discuss differentiable spaces, differentiable stratified spaces, and differentiable stratified groupoids. We will give examples of naturally occurring differentiable stratified groupoids and consider some of the consequences of these structures. Differentiable stratified groupoids (joint work with Carla Farsi and Markus Pflaum) Sponsored by the Meyer Fund
Nov. 18, 2014 11am (MATH 350)	Number Theory Bianca Viray (University of Washington) X In 1970, Manin showed that the Brauer group can obstruct the existence of rational points. Colliot-Th�l�ne and Sansuc have conjectured that this obstruction completely explains the failure of rational points on del Pezzo surfaces. We show that on degree 4 del Pezzo surfaces, this Brauer-Manin obstruction manifests itself through linear projections. As a consequence of the proof, we obtain a simple and efficient for computing the Brauer classes of a degree 4 del Pezzo surface. This is joint work with Anthony V�rilly-Alvarado. Obstructions to the Hasse principle on degree 4 del Pezzo surfaces
Nov. 18, 2014 12:10pm (MATH …	Kempner Robert Varley (University of Georgia) X Rational homotopy theory as developed by Quillen and Sullivan allows a complete description of its objects of study by differential graded algebras over the rational numbers. Thus rationally some of the basic classification problems in homotopy theory become "moduli problems" in algebraic geometry and number theory. Halperin, Schlessinger, and Stasheff showed how to describe all rational homotopy types having a given cohomology algebra. I will discuss this moduli construction and how completion of the rationals is useful for its analysis. In particular, homotopy theory over the finite adeles seems to accommodate the known fact that even for smooth projective varieties defined over a number field, the rational homotopy type of the associated topological space can depend on the embedding of the number field in the complex numbers. Rational homotopy theory and its completions
Nov. 18, 2014 3pm (Math 350)	Algebraic Geometry Robert Varley (University of Georgia) X I will recount some of the interesting features of principally polarized abelian varieties and their theta divisors, emphasizing the case of Jacobians of curves, connections with linear series, and the intensive study made by Kempf of the presentation matrix for the determinantal structure of Jacobian theta divisors. The analogous setup for Pryms is more complicated. Roy Smith and I have been trying to supplement Casalaina-Martin's multiplicity formula by using a natural geometric parametrization of the tangent cone. I will describe the skew-symmetric presentation matrix for the (local) Pfaffian structure of Prym theta divisors. It is then clear which essential higher order information is still lacking for very exceptional singular points, and I will explain how the unknown 2nd order terms seem to be governed by a Massey product structure. Towards understanding all the singular points of Prym theta divisors Sponsored by the Meyer Fund
Nov. 18, 2014 11pm (Math 220)	Noncomm Geometry Alex Nita Fredholm Modules
Nov. 19, 2014 4pm (MATH 350)	Grad Student Seminar Leo Herr (CU-Boulder) In Defense of Projective Space
Nov. 20, 2014 3pm (MATH 350)	Probability Ke Wang (IMA) X We start with a simple, yet useful, concentration inequality concerning random weighted projections in high dimensional spaces. The inequality is then used to prove a general concentration inequality for random quadratic forms. In another application, we show the optimal infinity norm O(sqrt{(log n)/n}) for most unit eigenvectors of a large class of random matrices, including the adjacency matrix of random graphs. This is joint work with Van Vu. Random weighted projections, random quadratic forms and random eigenvectors
Nov. 20, 2014 3pm (Weber 201…	Algebraic Geometry Maria Angelica Cueto (Columbia University) X The aim of my two talks will be to show that the tropical projective Grassmannian of planes is homeomorphic to a closed subset of the analytic Grassmannian in the sense of Berkovich. Our proof is constructive and it relies on the combinatorial description of the tropical Grassmannian as a space of phylogenetic trees by Speyer-Sturmfels. In the first talk, I will discuss the connection between tropical geometry and analytification of algebraic varieties, and explain the notion of faithful tropicalization. I will also describe the combinatorics of the aforementioned space of trees inside tropical projective space. The second talk will be devoted to the proof of the main theorem and its interpretation in terms of the tropicalization map. Namely, the fiber over each point is an affinoid domain with a unique Shilov boundary point. Our homeomorphism identifies points in the tropical Grassmannian with the unique Shilov boundary point on their fibers, allowing for further generalizations of our results by Gubler-Rabinoff-Werner. This is joint work with M. Haebich and A. Werner. Faithful tropicalization of the Grassmannian of planes
Dec. 01, 2014 4pm (MATH 350)	PDE/Analysis David Ebin (Stony Brook University) X We will consider the initial value problem for the motion of incompressible inviscid fluids with free boundary and surface tension on the boundary. We will show how to find solutions. We also show that If the initial boundary has constant mean curvature, then the motion converges to motion of a fluid with fixed boundary as the surface tension constant gets large. We shall also show that the absence of surface tension can lead to an ill-posed problem. The initial value problem for fluids with free boundary and surface tension Sponsored by the Meyer Fund
Dec. 02, 2014 11am (MATH 350)	Number Theory Doug Ulmer (Georgia Tech) X For every genus g>0 and most primes p, we write down a curve over Fp(t) with Jacobian of large rank and with explicit divisors to fill out a finite index subgroup of the Mordell-Weil group. The height pairings among the explicit points have a very nice group-theoretic description, and we have an analytic class number formula of the type \|sha\|=square of index of the explicit points in the full Mordell-Weil group. Explicit high ranks in higher genus
Dec. 02, 2014 2pm (MATH 350)	Lie Theory Katherine Stange (University of Colorado Boulder) X This is a number theory talk of interest to those who care about matrix groups. A Schmidt arrangement is the orbit of the real line under the Bianchi group PSL(2,OK) (realised as Mobius transformations) where OK is the ring of integers in an imaginary quadratic field K. The arrangement takes the form of a dense collection of intricately nested circles in the complex plane. I'll explain how the number theory of K influences the arrangement, and I'll use these arrangements to generalise Apollonian circle packings and define a new collection of thin groups of arithmetic interest. In other words, for those who walk the third floor, I will be explaining the circles on my door. The talk will require some basic algebraic number theory (e.g. the ideal class group), and a passing familiarity with Mobius transformations. The Apollonian structure of quadratic imaginary fields
Dec. 02, 2014 2pm (MATH 350)	Number Theory Katherine Stange (University of Colorado Boulder) X This is a number theory talk of interest to those who care about matrix groups.� A Schmidt arrangement is the orbit of the real line under the Bianchi group PSL(2,OK) (realised as Mobius transformations) where OK is the ring of integers in an imaginary quadratic field K.� The arrangement takes the form of a dense collection of intricately nested circles in the complex plane.� I'll explain how the number theory of K influences the arrangement, and I'll use these arrangements to generalise Apollonian circle packings and define a new collection of thin groups of arithmetic interest. In other words, for those who walk the third floor, I will be explaining the circles on my door.� The talk will require some basic algebraic number theory (e.g. the ideal class group), and a passing familiarity with Mobius transformations. (SPECIAL TIME) The Apollonian structure of quadratic imaginary fields / cross listed with Lie Theory Seminar
Dec. 02, 2014 3pm (Math 350)	Algebraic Geometry Martin Ulirsch (Brown University) X This talk will begin with a quick introduction to the topology of Berkovich analytic spaces and the tropical geometry of toric varieties. In particular, we are going to talk about skeletons of toric varieties and their relationship to tropicalization. Moreover, I am going to explain how a generalization of these notions to the setting of toroidal embeddings, open embeddings that are �tale locally isomorphic to the torus embedding of a toric variety, can be used to study the tropical geometry of moduli spaces. Part I: Tropicalization of toric varieties and moduli spaces Sponsored by the Meyer Fund
Dec. 02, 2014 4pm (Math 350)	Algebraic Geometry Martin Ulirsch (Brown University) X Recent work by J. and N. Giansiracusa, myself, and O. Lorscheid suggests that the tropical geometry of a toric variety X, or more generally of a logarithmic scheme X, can be formalized as a "Berkovich analytification" of a scheme over the field with one element that is canonically associated to X. The goal of this talk is to introduce the theory of Artin fans, originally due to D. Abramovich and J. Wise, which can be used to lift rather unwieldy F₁-geometric objects to the more familiar realm of algebraic stacks. Artin fans are �tale locally isomorphic to quotient stacks of toric varieties by their big tori and their glueing data has a completely combinatorial description in terms of Kato fans. I am going to explain how to use the ideas surrounding the notion Artin fans to study tropicalization maps associated to toric varieties and logarithmic schemes. Surprisingly these techniques allow us to give a reinterpretation of Tevelev's theory of tropical compactifications that can be generalized to compactifications of subvarieties in logarithmically smooth compactifcations of smooth varieties. For example, we can introduce definitions of tropical pairs and schoen varieties in terms of Artin fans that are equivalent to Tevelev's notions. Part II: Artin fans in tropical geometry Sponsored by the Meyer Fund
Dec. 02, 2014 11pm (Math 220)	Noncomm Geometry Alex Nita Fredholm Modules (continued)
Dec. 03, 2014 4pm (MATH 350)	Grad Student Seminar Steve Weinell (CU-Boulder) X In this talk we will attempt to state and then give a rough outline of the proof of G\"{o}del's first incompleteness theorem. We will explore the notions of G\"{o}del numbers and recursive functions and relations, along with explanations of basic concepts in mathematical logic as needed. We will then state without proof some key theorems and outline the proof of G\"{o}del's incompleteness. This talk will follow notes written by Dr. Don Monk. Godel's First Incompleteness Theorem
Dec. 09, 2014 9am (MATH 350)	PDE/Analysis Boris Khesin (University of Toronto) KAM theory and the 3D Euler equation Sponsored by the Meyer Fund
Dec. 09, 2014 2pm (Math 350)	Lie Theory Elizabeth Gillaspy X This talk will be a merged seminar of the "Analysis and Groupoids" seminar and the "Algebraic Lie Theory" seminar.� After a quick overview of the "deformations of Lie algebras" picture of quantum groups, I will introduce a few of the operator algebraic approaches of quantum groups. The idea of twisting a quantum group by a 2-cocycle has also received a fair amount of attention; I will explain this construction and discuss how it connects to the twisted groupoid C-algebras I have studied. Quantum Groups as C-algebras and Lie algebras Sponsored by the Meyer Fund
Dec. 09, 2014 2pm (Math 350)	Functional Analysis Elizabeth Gillaspy (University of Colorado - Boulder) X This talk will be a merged seminar of the "Analysis and Groupoids" seminar and the "Algebraic Lie Theory" seminar. After a quick overview of the "deformations of Lie algebras" picture of quantum groups, I will introduce a few of the operator algebraic approaches of quantum groups. The idea of twisting a quantum group by a 2-cocycle has also received a fair amount of attention; I will explain this construction and discuss how it connects to the twisted groupoid C-algebras I have studied. [joint with Algebraic Lie Theory] Quantum Groups as C-algebras and Lie algebras Sponsored by the Meyer Fund
Dec. 09, 2014 3pm (MATH 350)	Kempner Boris Khesin (University of Toronto) X A plane curve is called nondegenerate if it has no inflection points. How many classes of closed nondegenerate curves exist on a sphere? We are going to see how this geometric problem, solved in 1970, reappeared along with its generalizations in the context of the Korteweg-de Vries and Boussinesq equations. Its discrete version is related to the 2D pentagram map defined by R.Schwartz in 1992. We will also describe its generalizations, pentagram maps on polygons in any dimension and discuss their integrability properties. This is a joint work with Fedor Soloviev. Pentagram maps and nondegenerate curves Sponsored by the Meyer Fund
Dec. 09, 2014 11pm (Math 220)	Noncomm Geometry Alex Nita Fredholm Modules (continued)
Jan. 21, 2015 11am (Math 350)	Functional Analysis Sooran Kang (University of Otago) X We review KMS states on C-algebras associated to directed graphs and higher-rank graphs. Then� we discuss recent joint work with Iain Raeburn and Astrid an Huef� on spatial realizations of KMS states on C-algebras associated to higher-rank graphs. KMS states on C*-algebras associated to higher-rank graphs Sponsored by the Meyer Fund
Jan. 30, 2015 4pm (MATH 350)	PDE/Analysis Jae Min Lee (CU Boulder) X We show that if the dispersion of the KdV equation is replaced by a higher order dispersion $∂xm$ , where $m ≥ 3$ is an odd integer, then the critical Sobolev exponent for local well-posedness on the circle does not change. That is, the resulting equation is locally well-posed in $Hs(T)$ , $s ≥ -1/2$ . In this first talk, I will introduce the solution space for the IVP for KdV, state the lemmas, and state and prove the main theorem. Keywords: KdV equation, Local well-posedness, Sobolev spaces, Fourier transform. Well-posedness of KdV with higher dispersion - Part 1

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Events for September 2014 – January 2015

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Kempner

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Functional Analysis

Lie Theory

Algebraic Geometry

Noncomm Geometry

Grad Student Seminar

Probability

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Kempner

PDE/Analysis

Number Theory

Kempner

Lie Theory

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Algebraic Geometry

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Grad Student Seminar

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Kempner

Lie Theory

Noncomm Geometry

Algebraic Geometry

Probability

Functional Analysis

Number Theory

Kempner

Algebraic Geometry

Noncomm Geometry

Grad Student Seminar

Probability

Algebraic Geometry

PDE/Analysis

Number Theory