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Events for December 2013 – April 2014

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Apr. 12, 2014 12:52pm (HUMN …	Algebraic Geometry Western Algebraic Geometry Symposium WAGS April 12-13
Dec. 03, 2013 10am (MATH 350)	Ulam Thomas Ivey X I will review integration by the method of Darboux for second-order hyperbolic PDE in the plane, and its natural extension to hyperbolic exterior differential systems (EDS). I will then discuss the extension of this technique to decomposable EDS, as studied by Anderson, Fels and Vassiliou in their groundbreaking paper "Superposition Formulas for Exterior Differential Systems." Peter Vassiliou (University of Canberra) will be visiting the department this week and next, and this week's Ulam seminar is designed to provide background for Vassiliou's seminar talks next week. Generalizations of Darboux Integrability
Dec. 03, 2013 1pm (MATH 220)	Grad Algebra/Logic Charlie Scherer (CU Boulder) Diamonds are a Group's Best Friend, Part 2
Dec. 03, 2013 2pm (Math 350)	Lie Theory Bridget Tenner (DePaul University) X We will discuss two varieties of permutation patterns: classical patterns and the more generally (and more recently) defined mesh patterns. We will analyze completely when a mesh pattern is equivalent to a finite collection of classical patterns, in a sense declaring that the additional data of the mesh was superfluous for these patterns. We will also describe the permutations having the fewest superfluous meshes, and the permutations having the most, enumerating the superfluous meshes in each case. (Mesh) Patterns Sponsored by the Meyer Fund
Dec. 03, 2013 3pm (MATH 350)	PDE/Analysis Thomas Ivey X Austere submanifolds are a special sub-class of minimal submanifolds in Euclidean space. Harvey and Lawson defined this class, and showed that the conormal bundle of a submanifold M is special Lagrangian if and only if M is austere. Later, Bryant classified austere 3-folds in Euclidean space, as well as linear-algebraic models for austere 4-folds. More classification results in dimension four were obtained by Marianty Ionel and myself, and we have recently generalized the austere condition to submanifolds in complex projective space. An introduction to austere geometry
Dec. 09, 2013 4pm (MATH 350)	Kempner Anca Radulescu (CU Boulder) X Many natural systems, including the brain, are organized as dynamic networks, with nodes interacting in a time-dependent fashion. The way in which various parts of the brain (from the micro-scale of neurons to the macro-scale of functional regions) are wired together is one of the great scientific challenges of the 21st century, currently being addressed by large-scale research collaborations, such as the Human Connectome Project. The aim of our own research is to understand in particular the relationship between a networks hardwired circuitry and its dynamics. Key factors for optimal (critical) dynamics in a network of neural nodes are a combination of a well-balanced adjacency scheme together with well-tuned connection strengths between nodes. We investigate whether small perturbations in edge density or geometry can produce large effects in the systems phase space dynamics, or if phenomena like phase transitions (bifurcations) are robust to either of such changes. We finally illustrate, (using imaging results from 97 human subjects with a wide range of emotional responses) how such properties can be useful as biomarkers for different emotional profiles, or neuropsychiatric conditions. Graph theory, nonlinear networks and emotional responses
Dec. 10, 2013 1pm (MATH 220)	Grad Algebra/Logic Alexandr Kazda (Vanderbilt University) X There is a lot happening on the boundary between universal algebra and computer science. It is not very surprising that algebraists want to have fast algorithms. However, the connection runs in the other direction as well: It turns out that universal algebra is a very good tool for describing the complexity of the Constraint Satisfaction Problem (CSP). An instance of the CSP asks us to decide if we can assign values to variables in such a way that a list of constraints is satisfied (examples: graph coloring, logical formula satisfiability, Sudoku). If we restrict the sort of constraints to be used, the complexity of solving the CSP can vary from polynomial to NP-complete. We will talk about how to use universal algebra to classify the complexity of many such restricted CSPs. Universal Algebra Meets Algorithmic Complexity
Dec. 10, 2013 3pm (MATH 350)	PDE/Analysis Peter Vassiliou (University of Canberra, Australia) X ABSTRACT: Gaston Darboux (1842 - 1917) was much occupied with the theory of orthogonal coordinate systems throughout his productive career. Despite his many distinguished researchers as well as vast contributions by others like L. Bianchi (1856 -1928) and G. Lame (1795 - 1870) much remains to be understood and discovered. In this talk I will introduce the basic ideas and then go on to show how the theory of Darboux integrable systems can be used to construct orthogonal coordinate systems. It will be shown that there is a natural relationship between this circle of ideas and certain Einstein metrics as well as a particular completely integrable system, the so called $n$ -wave resonant interaction system. A number of open questions will be framed Einstein Meets Darboux
Dec. 14, 2013 4pm (MATH 350)	Ulam Jeff Taylor (CU Boulder) X This is my abstract This is a test Sponsored by the Meyer Fund
Jan. 01, 2014 3pm (Math 350)	Algebraic Geometry Previous talks Previous talks
Jan. 01, 2014 4pm (MATH 350)	Kempner Previous talks Previous talks
Jan. 23, 2014 2pm (MATH 350)	PDE/Analysis NA X Among other things, we will discuss topics and speakers for this semester's seminar. All are welcomed to attend. Organizational Meeting
Jan. 28, 2014 9am (MATH 350)	PDE/Analysis Alejandro Sarria (CU Boulder) X The two-component Camassa-Holm system models the propagation of unidirectional shallow water waves over a flat bed and, in some instances, admits an interpretation as a geodesic equation for a right-invariant metric on the diffeomorphism group. In this talk, a short-wave model for this system is studied with breakdown (or global existence in time) of classical solutions being discussed. On a short-wave model for the two-component Camassa-Holm system
Jan. 28, 2014 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Infinite Groups with Finite Conjugacy Classes, Part 1
Jan. 28, 2014 1pm (MATH 350)	Number Theory Jeff Thunder (University of Northern Illinois) X In his paper Northcott's Theorem on Heights II. The Quadratic Case, W.M. Schmidt gave asymptotic estimates for the number of points in projective space that have height no greater than a given bound and that generate a quadratic extension of the rational number field. For the special case where the points lie in projective 2-space, he needed to prove a result on sums of quotients of certain L-series (coming from quadratic extensions of the rational number field). Motivated by the function field case of Schmidt's result, we will look at L-series over function fields and discuss some recent results. L-series over function fields
Feb. 04, 2014 9am (MATH 350)	PDE/Analysis Pearce Washabaugh (CU Boulder) X The Euler-Arnold equation is essentially a coordinate invariant geodesic equation that can be written down on any Lie group, even those of infinite dimension, with a specific kind of inner product on its Lie algebra. I'll review and expand upon Boramey's introduction to this topic last semester. Time permitting I'll talk about curvature calculations on the group of volume preserving diffeomorphisms of a manifold with applications to weather prediction, as well as magnetic extensions of Lie groups, which allow one to phrase the system of ideal magnetohydrodynamics equations as geodesic equations on an infinite dimensional Lie group. An Introduction to the Euler-Arnold Equation
Feb. 04, 2014 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Infinite Groups with Finite Conjugacy Classes, Part 2
Feb. 11, 2014 9am (MATH 350)	PDE/Analysis Stephen C. Preston (CU Boulder) X I will give an overview of infinite-dimensional Riemannian geometry, especially those arising in physical applications. In particular I will discuss the sign of the curvature for the volume-preserving diffeomorphisms and the space of inextensible strings, and what it means. The talk will assume some knowledge of finite-dimensional Riemannian geometry but not much beyond that. Curvatures of infinite-dimensional manifolds -Part I
Feb. 11, 2014 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Infinite Groups with Finite Conjugacy Classes, Part 3
Feb. 18, 2014 9am (MATH 350)	PDE/Analysis Boramey Chhay (CU Boulder) X I will introduce an example of an infinite dimensional manifold which is the manifold of Riemannian metrics. That is, given a finite dimensional, compact, smooth, orientable manifold $M$ without boundary, we can consider the Riemannian structures that can be placed on $M$ . We will then put a metric on this space and discuss its properties. Metrics on the Space of Metrics - Part I
Feb. 25, 2014 9am (MATH 350)	PDE/Analysis Boramey Chhay (CU Boulder) X I will introduce an example of an infinite dimensional manifold which is the manifold of Riemannian metrics. That is, given a finite dimensional, compact, smooth, orientable manifold $M$ without boundary, we can consider the Riemannian structures that can be placed on $M$ . We will then put a metric on this space and discuss its properties. Metrics on the Space of Metrics - Part II
Feb. 25, 2014 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei (CU Boulder) Burnside's Theorem on Transitive Permutation Groups of Prime Degree, Part 1
Mar. 04, 2014 9am (MATH 350)	PDE/Analysis Taylor Joseph Klotz (CU Boulder) X Description: This talk will use the Ricci Flow to put curvature bounds on manifolds in three cases: Euler characteristic of a given surface is positive, zero, or negative. Using these bounds one can show that in each case the metric tends toward a limit metric on the surface that has constant curvature. This talk will focus on the latter two cases and if time permits the more difficult case of positive Euler characteristic will be discussed. Partial proof of the Uniformization Theorem using Ricci Flow
Mar. 04, 2014 1pm (MATH 220)	Grad Algebra/Logic Agnes Szendrei Burnside's Theorem on Transitive Permutation Groups of Prime Degree, Part 2
Mar. 04, 2014 2pm (MATH 350)	Lie Theory C. Ryan Vinroot X There are several very good reasons to understand the real-valued characters of finite groups of Lie type, including applications in the general theory of real characters of finite groups, and applications in the representations of p-adic group. In the case that $G$ is a connected reductive group with connected center, defined over a finite field by Frobenius morphism F, we are able to parameterize the real-valued characters of the finite group $G^{F}$ using the Lusztig parameters, or Jordan decomposition, of the characters. The main tool to prove this parameterization is by using a result of Digne and Michel, who describe the Jordan decomposition map as the unique such map with a certain list of properties, where this uniqueness can be exploited. The parameterization we obtain leads one to conjecture how to predict the Frobenius-Schur indicator of a real-valued character of $G^{F}$ . This work is joint work with Bhama Srinivasan from the University of Illinois at Chicago. Real-valued characters and Jordan decomposition Sponsored by the Meyer Fund
Mar. 10, 2014 12:10pm (MATH …	Kempner a David Zureick-Brown (Emory University) X TBA TBA
Mar. 10, 2014 12:10pm (MATH …	Kempner test tBA
Mar. 10, 2014 3pm (Math 350)	Algebraic Geometry David Zureick-Brown (Emory University) X TBA TBA
Mar. 10, 2014 4:10pm (MATH 3…	Kempner Hessel Posthuma (Korteweg-de Vries Institute, University of Amsterdam) X In this talk I will describe a cohomological version of the so-called Baum- Connes map which associates to any proper action of a Lie group a natural class of index theorems. These index theorems generalize various well-known classical cases such as the Atiyah-Singer index theorem and its variants. If time permits, I will explain the extension to groupoids. This talk is based on joint work with Markus Pflaum and Xiang Tang. Higher index theorems for proper actions
Mar. 10, 2014 5:10pm (MATH 3…	Kempner Xiang Tang ((Washington University)) X In this talk, we will discuss some recent progress about the problem of integration of exact Courant algebroids. We construct an infinite-dimensional symplectic 2-groupoid as the integration of an exact Courant algebroid. We show that every integrable Dirac structure integrates to a “Lagrangian” sub-2-groupoid of this symplectic 2-groupoid. This is joint work with Rajan Mehta. Integration of exact Courant algebroids
Mar. 11, 2014 9am (MATH 350)	PDE/Analysis Stephen C. Preston (CU Boulder) X I will give an overview of infinite-dimensional Riemannian geometry, especially those arising in physical applications. In particular I will discuss the sign of the curvature for the volume-preserving diffeomorphisms and the space of inextensible strings, and what it means. The talk will assume some knowledge of finite-dimensional Riemannian geometry but not much beyond that. Curvatures of infinite-dimensional manifolds - Part II
Mar. 11, 2014 1pm (MATH 350)	Number Theory Paula Tretkoff (Texas A&M University) X Calabi-Yau varieties are of interest to physics, due to their appearance in string theory, and in mathematics, thanks to the tractable nature of many examples on which one can do enumerative algebraic geometry and algebraic number theory. In both cases, identifying Calabi-Yau varieties related by mirror symmetry is important. Calabi-Yau varieties with complex multiplication have special properties useful for rational conformal field theory and number theory. Very little is known about the transcendence of periods of higher forms, and the abundance of examples of Calabi-Yau varieties makes them a good place to look for results on transcendence of such periods. We present some new results on normalized period matrices for higher forms which generalize to certain families of Calabi-Yau varieties Th. Schneider's criterion for CM on elliptic curves, which is a result from transcendental number theory. We focus on the so-called Borcea-Voisin towers that are of interest in mirror symmetry. Some preliminary results with M.D. Tretkoff were presented in a previous lecture in Boulder. Genuinely new results on unnormalized periods of higher forms on Calabi-Yau varieties remain out of reach for the moment, and we hope such problems will make for good discussions. We aim to make our talk fairly accessible. A criterion for complex multiplication on Calabi-Yau varieties
Mar. 12, 2014 4pm (MATH 350)	Grad Student Seminar Noah Williams (CU Boulder) X Origami, the art of paper folding, is hundreds of years old, and yet, it continues to evolve as we embrace its underlying mathematical structure. This talk will introduce some of the mathematical ideas prominent in paper folding, including a brief discussion of the Huzita-Justin axioms and an interactive demonstration in which we will trisect an angle and double a cube. Unfolding the Mathematics of Origami
Mar. 17, 2014 3:30pm (MATH 3…	Kempner P. Kutzko, R. Haas, A. Helminck, P. Willis (Iowa, Smith, NC State, Reasoning Mind In…) X Drs. Kutzko, Haas, and Helminck will talk about their efforts to increase the numbers of women and members of traditionally underrepresented minority groups in their institutions. Dr. Kutzko founded the National Alliance for Doctoral Studies in Mathematics and has won awards for his work at the University of Iowa, and Dr. Helminck, another leader in the National Alliance, has played a transformative role at North Carolina State University. Dr. Haas is one of the founders of the Smith College Mathematics Postbaccalaureate program, which helps serves as a bridge between undergraduate and graduate programs in mathe- matics for members of tradiationally underrepresented groups. Dr. Willis will discuss her experiences in the University of Iowa Ph.D. program, where she entered the program as a student without as much background in mathematics as most of her peers, and left with an NSF postdoctoral fellowship. Increasing the representation of traditionally underrepresented groups in mathematics Ph.D. programs in the US
Mar. 18, 2014 9am (MATH 350)	PDE/Analysis Marcelo M. Disconzi (Vanderbilt University) X We study the free boundary Euler equations in three spatial dimensions with surface tension. Under natural assumptions, we prove that solutions of the free boundary fluid motion converge to solutions of the Euler equations in a fixed domain when the coefficient of surface tension $κ$ tends to infinity. The well-posedness of the free-boundary equations under the relevant hypothesis for the study of the limit $κ → ∞$ is also established. This is joint work with David G. Ebin. The free boundary Euler equations with large surface tension Sponsored by the Meyer Fund
Mar. 18, 2014 1pm (MATH 350)	Number Theory David Masser (Universität Basel) X Functions such as $1 x(x-λ)$ can always be integrated (with respect to $x$ ) in ``elementary terms" involving logarithms and exponentials. But not $1 x(x-1)(x-λ)$ unless $λ=0,1$ . A more interesting example is $1 (x-1+λ 3)x(x-1)(x-λ)$ , which can be done also for $λ=1 +-3 2$ . In 1981 James Davenport claimed that an arbitrary such algebraic $f(x,λ)$ can be integrated for at most finitely many special complex values $λ$ (unless it can be integrated for a general value of $λ$ ). Umberto Zannier and I dare to hope for a full proof in the next couple of years; but for now I will content myself with a general discussion of the problem together with some of the key concepts involved in settling significant special cases. The unlikelihood of integrability in elementary terms
Mar. 18, 2014 2pm (MATH 350)	Lie Theory Eric Marberg (Stanford) X A vector species is a functor from the category of finite sets with bijections to vector spaces; informally, one can view this as a sequence of $S_{n}$ -modules, one for each natural number $n$ . A Hopf monoid (in the category of vector species) consists of a vector species with unit, counit, product, and coproduct morphisms satisfying several compatibility conditions, analogous to a graded Hopf algebra. In this talk I will discuss the structure theory of Hopf monoids exhibiting certain strong forms of self-duality, and explain some results which can be viewed as species analogues of Zelevinsky's classification of positive self-dual Hopf algebras. As applications, I will describe how such results can be used to provide a simple way of constructing and understanding the relationships between various Hopf algebras attached to towers of unipotent groups, recently considered in the literature. Strongly self-dual Hopf monoids in species with applications to combinatorial Hopf algebras Sponsored by the Meyer Fund
Mar. 18, 2014 3pm (Math 220)	Algebraic Geometry Maksym Fedorchuk (Boston College) X I will discuss a GIT problem concerning stability of syzygy points of canonical curves, and explain its solution for the first syzygy point in the generic case (joint with Deopurkar and Swinarski). I will also explain connections with Green's conjecture and applications related to the minimal model program for the moduli space of curves. Toward GIT stability of syzygies of canonical curves Sponsored by the Meyer Fund
Mar. 19, 2014 4pm (MATH 350)	Grad Student Seminar Dimitro Golovanich X Information transmission is a very large part of modern life, and so the problem of finding robust and reliable ways of encoding and decoding data is a pertinent one. In this talk we present a few of the most basic results in Coding Theory and (if the time allows) a few very simple (but nonetheless illuminating) examples of codes, some of which have neat decoding algorithms. Results in Coding Theory
Mar. 27, 2014 3pm (Weber 201…	Algebraic Geometry Mark Shoemaker (Utah) X Given a homogeneous degree five polynomial W in the variables X_1, . . . , X_5, we may view W as defining a quintic hypersurface in P^4 or alternatively, as defining a singularity in [C^5/Z_5], where the group action is diagonal. In the first case, one may consider the Gromov-Witten invariants of {W=0}. In the second case, there is a way to construct analogous invariants, called FJRW invariants, of the singularity. The LG/CY correspondence conjectures that these two sets of invariants are related. In this talk I will explain this correspondence, and its relation to a much older conjecture, the crepant resolution conjecture (CRC). I will sketch a proof that the CRC is equivalent to the LG/CY correspondence in certain cases using a generalization of the ``quantum Serre-duality'' of Coates-Givental. This work is joint with Y.-P. Lee and Nathan Priddis. A proof of the LG/CY correspondence via the crepant resolution conjecture
Apr. 01, 2014 1pm (MATH 350)	Number Theory Amy Feaver (CU Boulder) X TBA Euclid's Algorithm in Multiquadratic Fields (thesis defense)
Apr. 02, 2014 4pm (MATH 350)	Grad Student Seminar Justin Keller Topological Quantum Field Theories and ******-Algebras
Apr. 03, 2014 1pm (MATH 220)	Number Theory Lenny Fukshansky (Claremont College) X A celebrated theorem of Cassels (1955) asserts that an integral quadratic form, which is isotropic over Q, has a non-trivial integral zero of small height; the bound is in terms of the height of the coefficient vector of the quadratic form. In the later years, analogues of Cassels’ result have been proved over other global fields: over number fields by Raghavan (1975), over rational function fields by Prestel (1987), and over algebraic function fields by Pfister (1997). Further extensions of Cassels’ theorem to small-height isotropic subspaces of a quadratic space, using the contemporary theory of height functions as developed by W. M. Schmidt, have been obtained by Schlickewei (1985), Schlickewei & Schmidt (1987), and Vaaler (1987, 1989). More recently, I have done some work on effective (with respect to height) decompositions of bilinear spaces, as well as further generalization of this theory to the situations with additional algebraic conditions and over quaternion algebras. In this talk, I will discuss several results in this area, starting from Cassels’ original theorem and up until my own recent work. Some of the results discussed are joint work with W. K. Chan and G. Henshaw. Heights and effective theory of quadratic forms over global fields (NOTE: THURS)
Apr. 04, 2014 4pm (Benson 185)	Kempner Seth Sullivant (North Carolina State) X The main problem in phylogenetics is to reconstruct evolutionary relationships between collections of species, typically represented by a phylogenetic tree. In the statistical approach to phylogenetics, a probabilistic model of mutation is used to reconstruct the tree that best explains the data (the data consisting of DNA sequences from genes appearing in all species being analyzed). In algebraic statistics, we interpret these statistical models of evolution as geometric objects in a high-dimensional probability simplex. This connection arises because the functions that parametrize these models are polynomials, and hence we can consider statistical models as algebraic varieties. The goal of the talk is to introduce this connection and explain how the algebraic perspective leads to new theoretical advances in phylogenetics, and also provides new research directions in algebraic geometry. The talk material will be kept at an introductory level, with background on both phylogenetics and algebraic geometry. Phylogenetic algebraic geometry
Apr. 07, 2014 4pm (MATH 350)	Kempner Kyle Petersen (DePaul) X The face vector, or f-vector, of a simplicial complex counts the number of faces in the complex according to dimension (number of vertices, edges, triangles, etc.). An old problem in combinatorial topology is to characterize the f-vectors that can be realized for a given topological space. For example, there is no simplicial complex with 4 vertices and 7 edges (why not?), and while you can construct a simplicial complex with 5 vertices, 8 edges, and 5 triangles, such a complex cannot be realized on a sphere (this fact is deeper). In this talk, I describe some of the history of attempting to characterize f-vectors in the context of something called the Charney-Davis conjecture, which is itself a discretized version of a conjecture of Hopf. Due to work of S. Gal, the Charney-Davis conjecture follows if one can prove that a certain transformation of the f-vector is nonnegative. This is the gamma vector of the title. Interesting combinatorics ensue. What is the gamma vector? (And what does it count?)
Apr. 07, 2014 4pm (MATH 350)	Lie Theory Kyle Petersen (DePaul University) X The face vector, or f-vector, of a simplicial complex counts the number of faces in the complex according to dimension (number of vertices, edges, triangles, etc.). An old problem in combinatorial topology is to characterize the f-vectors that can be realized for a given topological space. For example, there is no simplicial complex with 4 vertices and 7 edges (why not?), and while you can construct a simplicial complex with 5 vertices, 8 edges, and 5 triangles, such a complex cannot be realized on a sphere (this fact is deeper). In this talk, I describe some of the history of attempting to characterize f-vectors in the context of something called the Charney-Davis conjecture, which is itself a discretized version of a conjecture of Hopf. Due to work of S. Gal, the Charney-Davis conjecture follows if one can prove that a certain transformation of the f-vector is nonnegative. This is the gamma vector of the title. Interesting combinatorics ensue. What is the gamma vector? (And what does it count?) Sponsored by the Meyer Fund
Apr. 08, 2014 9am (MATH 350)	PDE/Analysis Alejandro Sarria (CU Boulder) X The Constantin-Lax-Majda equation (CLM) was proposed as a one dimensional model for the three dimensional vorticity of an incompressible fluid. We provide background on the CLM model and discuss some of its drawbacks. Several of its proposed generalizations are also considered. In particular, blowup results and criteria leading to global solutions among these models are compared. The Constantin-Lax-Majda equation and generalizations thereof
Apr. 08, 2014 1pm (MATH 220)	Grad Algebra/Logic Jeffrey Shriner (CU Boulder) X A chip-firing game on a graph G begins with a configuration (the number of 'chips' on each vertex). When a vertex 'fires', it sends a chip to each adjacent vertex, so the only rule of the game is that a vertex may 'fire' if and only if it has at least deg(v) chips. We discuss a variant of the chip-firing game, called the dollar game, in which one vertex is required to always be in debt. Using the dollar game, we form an abelian group structure K(G), called the critical group of G. We compute the order of K(G), and look at how the dollar game may be used as a tool for analyzing the structure of the group. The Dollar Game and the Critical Group of a Graph, Part 1
Apr. 08, 2014 1pm (MATH 350)	Number Theory Rachel Davis (Purdue University) X Let $E$ be an elliptic curve over $ℚ$ with surjective mod-2 representation. Let $K$ be the splitting field of the $2$ -division polynomial of $E$ . We show that for every element $ξ$ of the cohomology group $H1(GQ,E[2])$ , there exists $E^{'}$ , a mod-2 companion of $E$ and $P ∈ E(Q)$ such that $E, P)$ maps to $ξ$ under the Kummer map. I will also discuss how a finite subgroup of this cohomology group is related to $S4$ -extensions of $ℚ$ that contain $K$ and are unramified outside a finite set of primes. (joint work with Edray Goins and Jamie Weigandt) Cohomology and S4 extensions of Q
Apr. 10, 2014 1pm (MATH 350)	Number Theory Damien Roy (University of Ottawa) X In a series of recent papers, W.M. Schmidt and L. Summerer develop a remarkable theory of parametric geometry of numbers which enables them to recover many results about simultaneous rational approximation to families of Q-linearly independent real numbers, or about the dual problem of forming small linear integer combinations of such numbers. They recover classical results of Khintchine and Jarnik as well as more recent results by Bugeaud and Laurent. They also find many new results of Diophantine approximation. Their theory provides constraints on the behavior of the successive minima of a natural family of one parameter convex bodies attached to a given n-tuple of real numbers, in terms of this varying parameter. In this talk, we are interested in the converse problem of constructing n-tuples of numbers for which the corresponding successive minima obey given behavior. We will present the general theory of Schmidt and Summerer, mention some applications, and report on recent progress concerning the above problem. On Schmidt and Summerer parametric geometry of numbers (NOTE: THURS)
Apr. 10, 2014 3pm (Webber 20…	Algebraic Geometry Dusty Ross (Michigan) X Given a quasi-homogeneous polynomial of degree d, Landau-Ginzburg theory studies certain intersection numbers on the moduli space of d-spin curves (parametrizing curves with d-th roots of the canonical bundle). I will describe a generalization of these intersection numbers obtained by allowing some of the points on the curves to be weighted in the sense of Hassett. As one changes the weights, the invariants thus obtained can be related by a wall-crossing formula. I will explain how the wall-crossing formula generalizes the mirror theorem of Chiodo-Iritani-Ruan, and in particular how it gives a completely enumerative (A-model) interpretation of the mirror phenomenon. Wall-crossing in genus zero Landau-Ginzburg theory
Apr. 14, 2014 10am (Eng E206…	Algebraic Geometry Douglas Ulmer (Georgia Tech) Jacobians with many points
Apr. 15, 2014 9am (MATH 350)	PDE/Analysis Boramey Chhay (CU Boulder) X I will introduce these two types of manifolds including basic definitions, properties, and applications. Contact and Symplectic Manifolds
Apr. 15, 2014 1pm (MATH 220)	Grad Algebra/Logic Jeffrey Shriner (CU Boulder) X A chip-firing game on a graph G begins with a configuration (the number of 'chips' on each vertex). When a vertex 'fires', it sends a chip to each adjacent vertex, so the only rule of the game is that a vertex may 'fire' if and only if it has at least deg(v) chips. We discuss a variant of the chip-firing game, called the dollar game, in which one vertex is required to always be in debt. Using the dollar game, we form an abelian group structure K(G), called the critical group of G. We compute the order of K(G), and look at how the dollar game may be used as a tool for analyzing the structure of the group. The Dollar Game and the Critical Group of a Graph, Part 2
Apr. 16, 2014 4pm (MATH 350)	Grad Student Seminar Jonathan Lamar X This sales pitch is loosely based on a paper of Barcelo and Ram (http://arxiv.org/abs/math/9707221), in which they attempt to describe the desired aesthetic of a result in combinatorial representation theory. I will do my best to communicate this aesthetic to you through two examples: the finite-dimensional representations of the symmetric groups, and the polynomial representations of GL(n,k) for k an algebraically closed field of characteristic zero. As it turns out, there is a nice combinatorial description of each theory. If time permits, I also hope to describe the relationship between the two examples using the language of polynomial functors. What Makes Representation Theory Combinatorial ?
Apr. 17, 2014 1pm (MATH 350)	Number Theory Gabrielle Nebe (RWTH Aachen) X This talk presents recent constructions and classifications of extremal even unimodular lattices whose dimension is a multiple of 24. We know six such lattices, the Leech lattice in dimension 24, four lattices of dimension 48 and, since 2010, also one extremal lattice in dimension 72. The existence of the latter was a longstanding open question. I will comment on its construction before turning to the classification of possible automorphisms of extremal even unimodular lattices in dimension 48. This investigation led to the discovery of a new extremal lattice, whose automorphism group is very small. Automorphisms of extremal lattices (NOTE: THURS)
Apr. 22, 2014 9am (MATH 350)	PDE/Analysis Steve Preston (CU Boulder) X Following up on Boramey Chhay's talk last week, I will discuss some geometry of the group of diffeomorphisms preserving a symplectic form or a contact structure. In particular I will talk about the geodesic equation in these spaces with a right-invariant Riemannian metric. Symplectomorphisms and contactomorphisms
Apr. 22, 2014 1pm (MATH 220)	Grad Algebra/Logic Jeffrey Shriner (CU Boulder) X A chip-firing game on a graph G begins with a configuration (the number of 'chips' on each vertex). When a vertex 'fires', it sends a chip to each adjacent vertex, so the only rule of the game is that a vertex may 'fire' if and only if it has at least deg(v) chips. We discuss a variant of the chip-firing game, called the dollar game, in which one vertex is required to always be in debt. Using the dollar game, we form an abelian group structure K(G), called the critical group of G. We compute the order of K(G), and look at how the dollar game may be used as a tool for analyzing the structure of the group. The Dollar Game and the Critical Group of a Graph, Part 3
Apr. 23, 2014 4pm (MATH 350)	Grad Student Seminar Xiaorong Liu X Stochastic functional differential equations is a kind of SDEs including past states of the solutions. I will present sufficient conditions ensuring the pth mean and almost sure exponential stability, as well as the pth mean integrability of solutions to stochastic functional differential equations. Moment exponential stability and integrability of stochastic functional differential equations
Apr. 28, 2014 4pm (MATH 350)	Kempner Hortensia Soto-Johnson (University of Northern Colorado) X One area of research in undergraduate mathematics education, which has not received much attention, is the teaching and learning of complex variables. In this presentation, I will share results from two projects related to research participants’ use of gesture as they conveyed their geometric reasoning about tasks related to complex variables. In the first study, we compared the gestures of six experts and four pairs of novices as they described their geometric reasoning of the complex number arithmetic operations z+w, zw, and 1/z. In the second project, we explored the interplay between gesture and diagrams as undergraduates reasoned about complex-valued equations. I will discuss the importance of gesture awareness in the classroom and directions for further research. Reasoning about complex variables concepts – the role of gesture
Apr. 29, 2014 9am (MATH 350)	PDE/Analysis Alejandro Sarria (CU Boulder) X We discuss a particular class of solutions to 3D Euler which blowup in finite time from smooth initial data. This family of exact solutions has infinite energy and was derived by Peter Constantin. Some qualitative properties of blowup are also addressed. Riccati Blowup in Semibounded Solutions to 3D Euler
Apr. 29, 2014 1pm (MATH 350)	Number Theory Hershy Kisilevsky (Concordia University) X For an elliptic curve $E$ defined over the rational field, $ℚ$ , we will be interested in the variation of the Mordell-Weil groups $E(K)$ as $K$ ranges over finite extensions of $ℚ$ . In particular we will examine the ranks of $E(K)$ (both algebraic and analytic), as $K$ varies and give some of our results and conjectures on the values obtained. Acquiring Algebraic Points on Elliptic Curves
Apr. 29, 2014 1pm (MATH 220)	Grad Algebra/Logic Michael Pinsker (Universite Diderot, Paris) X A function clone on a set D is a set of finitary operations on D which is closed under composition and which contains the projections. Every function clone carries a natural algebraic structure given by the equations that hold in the clone, as well as a natural topological structure given by pointwise convergence. Let P be the function clone consisting of all projections on a two-element set. Given any function clone C on a countably infinite set, we compare the following questions: 1) Is there a homomorphism from C to P? 2) Is there a continuous homomorphism from C to P? These questions have applications in constraint satisfaction. More context will be provided in the subsequent talk in the logic seminar. Decomposing function clones on infinite sets Sponsored by the Meyer Fund
Apr. 29, 2014 2pm (MATH 350)	Lie Theory Jonathan Lamar (CU) X I will be presenting on a paper of Halasi and Palfy in which they prove that for certain pattern subgroups of UT(n,q), the number of conjugacy classes is not given by a polynomial equation in q. Moreover, they also prove that for some pattern groups, the number of conjugacy classes is not given by even a finite set of polynomials in q. This result is related to a famous open problem posed by Graham Higman, who asked if the number of conjugacy classes of UT(n,q) is given by a polynomial in q. Pattern groups whose number of conjugacy classes is not given by a polynomial
Apr. 29, 2014 2pm (MATH 220)	Michael Pinsker (Universite Diderot, Paris) X The Constraint Satisfaction Problem (CSP) of a finite or countable first-order structure S in a finite relational language is the problem of deciding whether a given conjunction of atomic formulas in that language is satisfiable in S. Many classical computational problems can be modelled this way. The study of CSPs involves an interesting combination of techniques from universal algebra, Ramsey theory, and model theory. This talk will present an overview over these techniques as well as some wild conjectures. Introduction to Constraint Satisfaction over infinite structures Sponsored by the Meyer Fund
Apr. 29, 2014 3pm (Math 220)	Algebraic Geometry Samouil Molcho (Brown) X The space of stable log maps of Abramovich-Chen and Gross-Siebert is a central object of study in singular Gromov-Witten theory. In this talk, I will give an explicit combinatorial description of the space of genus 0, 2 pointed stable maps to a toric variety: it is an appropriate enrichment of the Chow Quotient of Kapranov-Sturmfels-Zelevinsky into a toric stack. The idea for this description comes from Morse Theory. This is joint work with William Gillam. Logarithmic Stable Maps as Moduli of Broken Orbits Sponsored by the Meyer Fund
Apr. 30, 2014 4pm (MATH 350)	Grad Student Seminar Trevor Jack X Cantor Spaces are precisely those spaces that are totally disconnected, compact metric spaces with no isolated points and this discussion will determine the number of nonequivalent metrics that can be defined on such spaces. Nonequivalent Metrics on Cantor Spaces

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Events for December 2013 – April 2014

Algebraic Geometry

Ulam

Grad Algebra/Logic

Lie Theory

PDE/Analysis

Kempner

Grad Algebra/Logic

PDE/Analysis

Ulam

Algebraic Geometry

Kempner

PDE/Analysis

PDE/Analysis

Grad Algebra/Logic

Number Theory

PDE/Analysis

Grad Algebra/Logic

PDE/Analysis

Grad Algebra/Logic

PDE/Analysis

PDE/Analysis

Grad Algebra/Logic

PDE/Analysis

Grad Algebra/Logic

Lie Theory

Kempner

Kempner

Algebraic Geometry

Kempner

Kempner

PDE/Analysis

Number Theory

Grad Student Seminar

Kempner

PDE/Analysis

Number Theory

Lie Theory

Algebraic Geometry

Grad Student Seminar

Algebraic Geometry

Number Theory

Grad Student Seminar

Number Theory

Kempner

Kempner

Lie Theory

PDE/Analysis

Grad Algebra/Logic

Number Theory

Number Theory

Algebraic Geometry

Algebraic Geometry

PDE/Analysis

Grad Algebra/Logic

Grad Student Seminar

Number Theory

PDE/Analysis

Grad Algebra/Logic

Grad Student Seminar

Kempner

PDE/Analysis

Number Theory

Grad Algebra/Logic

Lie Theory

Algebraic Geometry

Grad Student Seminar