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Events for October 2014 – February 2015

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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 11am (Math 220)	Noncomm Geometry Joseph Migler Introduction to K-theory and K-homology
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. 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 11am (Math 220)	Noncomm Geometry Joseph Migler Introduction to K-theory and K-homology (continued).
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. 21, 2014 11am (Math 220)	Noncomm Geometry Joseph Migler Introduction to K-theory and K-homology (continued).
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 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 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. 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 220)	Noncomm Geometry Alex Nita Fredholm Modules
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. 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 11am (Math 220)	Noncomm Geometry Raphaël 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. 04, 2014 3pm (Math 350)	Algebraic Geometry Pál Zsámboki (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 Pál Zsámboki (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. 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 220)	Noncomm Geometry Josh Frinak X If is morphism of complex vector bundles over a smooth manifold which is an isomorphism over a subset , then determines a class in the relative -group . I intend to present Quillen's construction of the Chern character which involves the use of a -graded variant of the concept of a connection called a superconnection. Given a convenient choice of superconnection we are interested in the curvature . It will turn out that the super trace of will represent the Chern character, , in de Rham cohomology. Chern character via superconnections.
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 , , for , but also to the context of complex maps , parametrized as , with . 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, and , iterated according to a prescribed binary sequence of s and 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. 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 220)	Noncomm Geometry Alex Nita Fredholm Modules
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-Thélène 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 Várilly-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. 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 220)	Noncomm Geometry Alex Nita Fredholm Modules (continued)
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 étale 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 étale 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. 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 11am (Math 220)	Noncomm Geometry Alex Nita Fredholm Modules (continued)
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
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 , where 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 , . 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
Feb. 03, 2015 1pm (MATH 220)	Grad Algebra/Logic Jason Hill (CU Boulder (doctoral candidate) and SpotXchange (data scientist)) X The aim of these talks is to discuss the algorithms and data structures used to examine finite permutation groups, and to question where parallel processing can be a benefit. In the first talk, we'll aim to answer the following questions: How are permutations stored and multiplied on a computer? How are permutation groups stored, and how do we determine invariants such as group order? How are stabilizer subgroups computed? Parallel Permutation Group Algorithms
Feb. 03, 2015 2pm (Math 220)	Functional Analysis Marty Walter (University of Colorado, Boulder) Negative Definite Functions Sponsored by the Meyer Fund
Feb. 04, 2015 9am (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 , where 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 , . In this second talk, the results leading to the main Theorem (proved in Part 1) will be established. Keywords: KdV equation, Local well-posedness, Sobolev spaces, Fourier transform. Well-posedness of KdV with higher dispersion - Part 2
Feb. 04, 2015 4pm (MATH 350)	Grad Student Seminar Robert Hines (CU-Boulder) X e is transcendental [and maybe pi -PIZZA PIE- not that I'd describe Blackjack pizza as transcendent, but I digress]. You know that e is transcendental, right? Have you seen a proof? Well here's your big chance! We'll warm up by showing that e is irrational and proving the existence of transcendental numbers (a la Liouville). Hermite's (1873) proof of the transcendence of e uses nothing more than basic calculus, arithmetic, and a heaping tablespoon of genius. Time permitting (or forcing), we will discuss generalizations due to Lindemann-Weierstrass, Gelfond-Schneider, and Baker. Trancendenz
Feb. 10, 2015 11am (MATH 350)	Number Theory Rachel Pries (Colorado State University) X We study the relationship between the p-rank of a curve and the p-ranks of the Prym varieties of its cyclic covers in characteristic p >0. For all p and g, we generalize a result of Nakajima by proving that the Prym varieties of all unramified cyclic degree L covers of a generic curve X of genus g and p-rank f are ordinary. When p > 3, we prove that there exists a curve of genus g and p-rank f having an unramified degree 2 cover whose Prym is almost ordinary. Using work of Raynaud, we use these two theorems to prove results about the (non)-intersection of the L-torsion group scheme with the theta divisor of the Jacobian of a generic curve X of genus g and p-rank f. On the existence of ordinary and almost ordinary Pryms
Feb. 10, 2015 12:10pm (MATH …	Kempner Jim Carlson (University of Utah) X As Cantor showed us, there are uncountably many transcendental numbers. Despite being overwhelmingly more numerous than algebraic numbers, it is not so easy to find them in Nature: we know, for example, that pi is transcendental, but proving this is a major result. We will discuss these facts, then go on to discuss the Kontsevich-Zagier theory that most transcendentals belong to a countable class, the periods of integrals of algebraic functions with rational coefficients. Finally, we consider Yoshinaga’s number: a specific number that is not a period. Transcendental numbers and periods
Feb. 10, 2015 1pm (MATH 220)	Grad Algebra/Logic Jason Hill (CU Boulder (doctoral candidate) and SpotXchange (data scientist)) Parallel Permutation Group Algorithms
Feb. 10, 2015 2pm (MATH 350)	Lie Theory Nat Thiem (CU) X This talk is an introduction to random walks on groups and some of the tools in representation theory used to study these walks. In particular, we will explore conditions under which a group's representation theory can still be used to study clumped variants of the group walk. At the heart of this talk is a family of unipotent groups, whose walks have a wide variety of flavors, including walks on positive integers, hypercubes, bounded partitions and more. This work is joint with Theplertboon. Superclass walks on unipotent groups
Feb. 10, 2015 3pm (Math 220)	Functional Analysis Judith Packer (University of Colorado, Boulder) X We review the quantum Heisenberg manifolds of M. Rieffel, who originally defined them as generalized fixed point algebras. These are shown to be twisted groupoid algebras as first defined by A. Kumjian. This is joint work with S. Kang and A. Kumjian. Quantum Heisenberg manifolds as twisted groupoid algebras Sponsored by the Meyer Fund
Feb. 11, 2015 4pm (MATH 350)	Grad Student Seminar Christian Klevdal X For topological spaces that are "nice" (by which we mean semi-locally simply connected), there is a close connection between covering spaces and the fundamental group. In this talk we will explain this relationship and show how it fails for more general spaces. We will then discuss some potential ways to generalize the theory. As far as background, we assume only basic knowledge of the fundamental group and covering spaces. The Hawai'ian Earring
Feb. 12, 2015 3pm (Webber 20…	Algebraic Geometry Jim Carlson (University of Utah) X As Cantor showed us, there are uncountably many transcendental numbers. Despite being overwhelmingly more numerous than algebraic numbers, it is not so easy to find them in Nature: we know, for example, that pi is transcendental, but proving this is a major result. We will discuss these facts, then go on to discuss the Kontsevich-Zagier theory that most transcendental belong to a countable class, the periods of integrals of algebraic functions with rational coefficients. Finally, we consider Yoshinaga’s number: a specific number that is not a period. Transcendental numbers and periods
Feb. 12, 2015 3pm (MATH 350)	Probability Sean O'Rourke (CU Boulder) X The famous Gauss-Lucas theorem describes a geometric connection between the roots of a polynomial and the roots of its derivative. In particular, the theorem states that the critical points of a polynomial p all lie within the convex hull of the roots of p. Building on the works of Pemantle-Rivin and Kabluchko, I will describe a probabilistic version of the Gauss-Lucas theorem, which holds for a large class of random polynomials. Critical points of random polynomials
Feb. 13, 2015 3pm (ECCR 265)	Kempner Andrea Bertozzi (UCLA) X Note the unusual time and place! Modeling of particle laden flow, especially in the case of higher particle concentrations, does not readily allow for first principles models. Rather, semi-empirical models of the bulk dynamics require careful comparision with experiments. At UCLA we have developed this theory for the geometry of viscous thin film flow with non-neutrally buoyant particles. We have found that for these slower flows, that diffusive flux models, involving a balance between shear-induced migration and hindered settling, can provide reasonably accurate predictive models. I will discuss the current state of this work including recent extensions to bidensity slurries and the relevant mathematics needed to understand the dynamics. Lubrication theory can be derived for this problem and results in a coupled system of conservation laws including regular shock dynamics and singular shocks. I will also briefly discuss relevant applications such as spiral separators. Particle laden thin films: theory and experiment
CANCELED Feb. 16, 2015	Jeff Taylor Test - please ignore
Feb. 17, 2015 12:10pm (MATH …	Kempner Piotr M. Hajac (Polish Academy of Sciences) X Assuming that both temperature and pressure are continuous functions, we can conclude that there are always two antipodal points on Earth with exactly the same pressure and temperature. This is the two-dimensional version of the celebrated Borsuk-Ulam Theorem which states that for any continuous map from the n-dimensional sphere to n-dimensional real Euclidean space there is always a pair of antipodal points on the sphere that are identified by the map. Our quest to unravel topological mysteries in the Middle Earth of quantum spaces will begin with gentle preparations in the Shire of elementary topology. Then, after riding swiftly through the Rohan of C-algebras and Gelfand-Naimark Theorems and carefully avoiding the Mordor of incomprehensible technicalities, we shall arrive in the Gondor of compact quantum groups acting on unital C-algebras. It is therein that the generalized Borsuk-Ulam-type statements dwell waiting to be proven or disproven. Time permitting, we shall pay tribute to the ancient quantum group SUq(2), and show how the proven non-trivializability of the SUq(2)-principal instanton bundle is a special case of two different noncommutative Borsuk-Ulam-type conjectures. (Based on joint work with Paul F. Baum and Ludwik Dabrowski.) There and back again: from the Borsuk-Ulam theorem to quantum spaces
Feb. 17, 2015 1pm (MATH 220)	Grad Algebra/Logic Jason Hill (CU Boulder (doctoral candidate) and SpotXchange (data scientist)) Parallel Permutation Group Algorithms
Feb. 17, 2015 2pm (MATH 350)	Lie Theory Martin Walter (CU) X Two years ago a student in Nat's class was also in mine and asked to do an independent study. One thing led to another and what I thought was going to be an easy question of functional analysis about abelian groups turned out to be mostly about number theory which perhaps everyone knows, even me, now. The answer: ``It'' is a negative definite function. A Special Negative Definite Function
Feb. 18, 2015 4pm (MATH 350)	Grad Student Seminar Aleesha Moran (CU-Boulder) X Numerical semigroups have long been studied for their interesting algebraic properties. Given a numerical semigroup and , the collection of arithmetic sequences with step size contained in naturally forms a monoid, denoted as . We refer to these monoids as Leamer monoids. These monoids were originally constructed to study special cases of the Huneke-Wiegand conjecture. We provide foundational results for the factorization theory of Leamer monoids, including a full description of their elasticities. We also give a complete description of the Leamer monoid when is generated by an arithmetic sequence with step size . We also study the collections of numerical semigroups which generate the same Leamer Monoid. Factorization Properties of Leamer Monoids
Feb. 19, 2015 12:10pm (MATH …	Kempner Alison Reddy (University of Illinois Urbana-Champaign) X Placing students into an appropriate first math course is conducive to their success in the first two years of college, while placement into the wrong course can have devastating effects. Accurate placement requires an accurate and recent assessment, but many students are placed based on standard test scores that are years out of date. Alison Reddy will discuss what makes a good placement program and give data the from the University of Illinois Placement Program which has assessed over 70,000 students over the past 8 years. Appropriate placement of students into a first math course: Placement program best practices
Feb. 19, 2015 3pm (MATH 350)	Probability Iddo Ben-Ari (U. Connecticut) X Consider Brownian motion on a bounded interval which is redistributed back into the interval whenever hitting the boundary. The redistribution from each boundary point is according to some fixed probability distribution associated with it, and, conditioned on the boundary point ``hit", the redistribution is independent of the past. It is not hard to show that this is an exponentially ergodic Markov process. The convergence rate has an analytic characterization as the spectral gap for an operator that can be viewed as the infinitesimal generator of the process. In some distinguished cases the gap has an explicit numerical expression. The main thrust of the work presented is to provide a probabilistic and intuitive interpretation for the convergence rate through construction of an efficient coupling, that is a coupling in which time for coupling has a tail that coincides with the convergence rate. The coupling is elementary but obtaining efficiency is not straightforward due to the fact that the redistribution ``reshuffles" the system. This is in sharp contrast with reflected BM on an interval for which it is well known that essentially any coupling is efficient. Time permitting, I will also discuss probabilistic treatment of spectral problems for related models. Efficient Coupling for Diffusion with Redistribution
Feb. 24, 2015 11am (MATH 350)	Number Theory Jeff Achter (Colorado State University) X An isogeny class of elliptic curves over a finite field is determined by a quadratic Weil polynomial. Gekeler has given a beautiful product formula, purely in terms of congruence considerations involving that polynomial, for the size of such an isogeny class; an equidistribution hypothesis too strong to be true apparently calculates this cardinality! I will give a new, transparent explanation, worked out with Julia Gordon, for this phenomenon. It turns out that Gekeler's formula computes an adelic orbital integral which, thanks to work of Langlands and Kottwitz, visibly calculates the desired quantity. Local heuristics and exact formulas for elliptic curves over finite fields
Feb. 24, 2015 3pm (Math 220)	Functional Analysis Ian Long (University of Colorado, Boulder) X A finite measure on the real line is said to be spectral if there exists a set of exponential functions which forms an orthonormal basis for . Moreover, a bounded Lebesgue measurable set of positive measure is spectral if the renormalization of Lebesgue measure on is spectral. I will introduce examples of spectral measures and sets on the real line, describe their relation to an unproven conjecture of Fuglede, examine a related conjecture made by Gabardo and Lai, and introduce a recent result by Duktay and Jorgensen which attempts to answer the question: when do two spectral measures Spectral Measures Sponsored by the Meyer Fund
Feb. 24, 2015 3pm (Math 350)	Algebraic Geometry Zheng Zhang (Stony Brook) X Based on the work of Gross and Sheng-Zuo, Friedman and Laza have classified variations of real Hodge structure of Calabi-Yau type over Hermitian symmetric domains. In particular, over every irreducible Hermitian symmetric domain there exists a canonical variation of real Hodge structure of Calabi-Yau type. In this talk, we will first review Friedman and Laza’s classification. A natural question to ask is whether the canonical Hermitian variations of Hodge structure of Calabi-Yau type come from families of Calabi-Yau manifolds (geometric realization). In general, this is very difficult and is still open for small dimensional domains. We will discuss an intermediate question, namely does the canonical variations occur in algebraic geometry as sub-variations of Hodge structure of those coming from families of algebraic varieties (motivic realization). In particular, we will give motivic realizations for the canonical variations of Calabi-Yau type over irreducible tube domains of type A using abelian varieties of Weil type. On motivic realizations for variations of Hodge structure of Calabi-Yau type over Hermitian symmetric domains Sponsored by the Meyer Fund
Feb. 25, 2015 5pm (MATH 350)	Grad Student Seminar Keli Parker (CU-Boulder) X In this brief talk I would like to go over some of the basics of blowing up in algebraic geometry and provide some explicit examples that arise when thinking about families of curves. For this first Slow Pitch of 2015 I would like to the keep the discussion at the introductory level, and there should be very little background knowledge needed. Note the late start (5pm). Blowing up with a view toward stable reduction
Feb. 26, 2015 3pm (MATH 350)	Probability Hyun Lee (CRM) X Interacting particle systems on the integer lattice that the coordinate Bethe Ansatz method can be applied to have connections to the random matrix theory and the symmetric function theory. We will survey the Bethe Ansatz method, and some known results and recent progresses in this direction. In particular, we will consider two initial configurations of the systems that are related to the GUE Tracy-Widom distribution and the GOE Tracy-Widom distribution. The coordinate Bethe Ansatz solvable interacting particle systems

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Events for October 2014 – February 2015

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