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Events for November 2013 – March 2014

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Nov. 05, 2013 7:31pm (Math 3…	Lie Theory Erica Shannon (CU) X The simple Lie algebra d_n has three minuscule representations: the natural representation and the two spin representations. I'll explain how to construct the Lie algebra d_n and how to use actions on polytopes to build these three representations. This talk will be as concrete as possible given that the smallest example is when n=4. No background knowledge of Lie algebras or representation theory will be assumed. Minuscule Representations of d_n via Polytopes
Nov. 05, 2013 10am (MATH 350)	Ulam Thomas Ivey X I'll give a broad introduction to the subject of integrablesystems of PDE. While there is no clear-cut definition of integrability, the most well-known integrable equations share several common features which I will review: soliton solutions, Lax pairs, Backlund transformations, and bi-Hamiltonian structures leading to infinitely many conservation laws and commuting flows. Integrable PDE, part 1
Nov. 05, 2013 1pm (MATH 220)	Grad Algebra/Logic Clifford Bridges (CU Boulder) A Method to Realize Groups as Galois groups: Rigidity in A_n, Part 3
Nov. 05, 2013 1pm (MATH 350)	Number Theory Stefan Erickson X A fundamental question in number theory is enumerating number fields and function fields with discriminant up to some bound. While the situation for quadratic fields is fairly straightforward, cubic fields pose a greater challenge. After a brief introduction to zeta functions and function fields, we will describe the techniques behind enumerating cubic function fields with a given quadratic resolvent, building on the work of Cohen-Morra for cubic number fields. This is joint work with Colin Weir (Simon Frasier) and Ravi Donepudi (Colorado College). Enumerating Cubic Function Fields
Nov. 05, 2013 3pm (Math 350)	Algebraic Geometry Anton Dzhamay (University of Northern Colorado) X The goal of this talk is to describe some interesting geometry that underlines a special class of discrete integrable systems known as discrete Painlevé equations. In the first hour we'll consider some concrete examples that we then use as a motivation for the general introduction into the Sakai's theory of classification of discrete Painlevé equations using the Okamoto surface of the equation. In the second hour we'll describe various sources of such equations and then show how the underlying geometry can help us relate different equations of the same type, up to finding very explicit change of coordinates that transforms one equation into the other. On the geometry of discrete Painlevé equations
Nov. 05, 2013 3pm (MATH 350)	PDE/Analysis Taylor Klotz (University of Colorado at Boulder) X The Ricci Flow has become a famous topic for its role in the solution of the Poincare conjecture which is a special case of the Geometrization conjecture. We will begin with the statement of these famous conjectures, briefly discuss the relationship to the Ricci Flow, and then present some special solutions. Ideas of Perelman's work on the topic may be mentioned but specific details will not be covered. Some Basics of Ricci Flow
Nov. 11, 2013 2pm (MATH 220)	H. Peter Gumm (Philipps-University, Marburg) Modal logics, coalgebraicallly
Nov. 11, 2013 3pm (Math 350)	Algebraic Geometry Anton Dzhamay (UNCO) X Abstract: The goal of this talk is to describe some interesting geometry that underlines a special class of discrete integrable systems known as discrete Painlevé equations. In the first hour we'll consider some concrete examples that we then use as a motivation for the general introduction into the Sakai's theory of classification of discrete Painlevé equations using the Okamoto surface of the equation. In the second hour we'll describe various sources of such equations and then show how the underlying geometry can help us relate different equations of the same type, up to finding very explicit change of coordinates that transforms one equation into the other. On the Geometry of Discrete Painlevé Equations
Nov. 12, 2013 10am (MATH 350)	Ulam Pearce Washabaugh X We will describe techniques to solve the forward and inverse scattering problems for the Schrödinger Operator, and then discuss how these can be used to solve the KdV equation. An Introduction to the Inverse Scattering Transform
Nov. 12, 2013 1pm (MATH 220)	Grad Algebra/Logic Heinz Peter Gumm (Philipps-University, Marburg, Germany, and Chapman University, Ora…) X Universal Co-Algebra is a general theory of state based systems, encompassing familiar structures, such as automata, Kripke Structures, dynamical systems, stochastic automata, even topological spaces considered as doubly nondeterministic transition systems. In order to capture and generalize systems with such diverse behaviours, the mathematical language to deal with universal coalgebra is Category theory. The results obtained this way are very concrete: homomorphism theorems, Birkhoff style theorems, classification theorems, and they can be very elegantly derived, using only elementary categorical notions and tools. Universal Co-Algebra is in many ways dual to Universal Algebra, and when translating co-algebraic proofs, one even obtains elegant proofs of universal algebraic results, albeit in a more general setting than that of classical universal algebra. Universal Co-Algebra
Nov. 12, 2013 1pm (MATH 350)	Number Theory Phillip Habegger X Conjectures on unlikely intersections generalize various problems in diophantine geometry such as the Manin-Mumford Conjecture. They originated in work of Bombieri-Masser-Zannier, Pink, and Zilber. Using a point counting result of Pila-Wilkie formulated in the language of o-minimal structures, Zannier devised a new strategy to prove the Manin-Mumford Conjecture. After providing some historical background on unlikely intersections I will explain what an o-minimal structures is. Then I'll describe a possible approach for dealing with higher dimensional unlikely intersections in abelian varieties defined over number fields. This is joint work in progress with Jonathan Pila. Unlikely Intersections and o-Minimal Structures
Nov. 12, 2013 2pm (MATH 350)	Lie Theory Uriya First (Hebrew University) X In short: I will explain how to use bilinear forms to prove theorems of Albert and Saltman about algebras with involution as well as several other related results. In detail: A well-known theorem of Albert states that a central simple algebra A of period 2 in the Brauer group admits an involution of the first kind (i.e. fixing the center). This was generalized by Saltman to Azumaya algebras with the difference that the conclusion is that there is some algebra in the Brauer class of A admitting an involution of the first kind. Albert and Saltman also gave necessary and sufficient conditions for existence of involutions of the second kind (i.e. not fixing the center). Another proof of Saltman's Theorem was later given by Knus, Parimala and Srinivas. I will discuss a new approach to Saltman's Theorem based on bilinear forms. This approach gives a new perspective on the proof of Knus-Parimala-Srinivas and also give rise to further results and generalizations. I shall also explain how to apply this approach to construct Azumaya algebras of period 2without involution. All notions (e.g. Brauer Group, Azumaya algebra) will be defined during the talk. Azumaya Algebras With and Without Involution
Nov. 12, 2013 3pm (MATH 220)	PDE/Analysis Jiahong Wu (Oklahoma State University) X The Boussinesq equations concerned here model geophysical flows such as atmospheric fronts and ocean circulations. Mathematically the 2D Boussinesq equations serve as a lower-dimensional model of the 3D hydrodynamics equations. In fact, the 2D Boussinesq equations retain some key features of the 3D Euler and the Navier-Stokes equations such as the vortex stretching mechanism. The global regularity problem on the 2D Boussinesq equations with partial or fractional dissipation has attracted considerable attention in the last few years. This talk reviews recent results on various cases of partial dissipation and presents most recent developments on the 2D Boussinesq equations with partial and fractional dissipation. Recent developments on the 2D Boussinesq equations with partial dissipation
Nov. 12, 2013 3pm (MATH 350)	Algebraic Geometry Qile Chen (Columbia) X The theory of stable log maps are developed for studying the degeneration of Gromov-Witten invariants. In this talk, I will introduce another interesting application of stable log maps to classicalbirational geometry ---- We construct very free rational curves on Fano complete intersections in projective spaces over an algebraically closed field of arbitrary characteristics. This a joint work with Yi Zhu. Very free rational curves on Fano complete intersections
Nov. 19, 2013 10am (MATH 350)	Ulam Thomas Ivey X I'll continue a broad introduction to the subject of integrable systems of PDE. I'll discuss the construction of an infinite sequence of commuting flows and local conservation laws for the KdV equation, and if time permits I will also Backlund transformations, which can be used to construct multi-soliton solutions. Integrable PDE, part 2
Nov. 19, 2013 1pm (MATH 220)	Grad Algebra/Logic Charlie Scherer (CU Boulder) X Whitehead's problem is a question about abelian groups that was motivated by complex analysis via homology and eventually resolved by set theory. I use the word "resolved" rather than "solved" because it was shown that Whitehead's problem is undecidable using ordinary mathematics (ZFC). I want to discuss Whitehead's problem as an example of how Jensen's diamond principle from set theory can be applied in algebra. This week I will state Whitehead's problem and give the solution for countable groups. Diamonds are a Group's Best Friend, Part 1
Nov. 19, 2013 1pm (MATH 350)	Number Theory Mehmet Kiral (Brown University) X Given a modular form $f$ , the corresponding $L$ -function $L(s,f)$ satisfies a functional equation as $s ↦ 1-s$ . One can view bounds of the form $L(1/2,f)$ as improvements towards the $α =0$ case, the Lindelof Hypothesis. The functional equation together with the Phragmen Lindelof theorem give the bound for $α = 1/4$ . This is called the convexity bound, and any result with $α < 1 / 4$ is called the subconvexity result. The Lindelof Hypothesis is a consequence of the Riemann Hypothesis for $L(s,f)$ and thus are expected to be true for all L-functions with a functional equation and an Euler product. We prove a subconvexity bound for $L(1/2,f,χ)$ in the conductor aspect where f is a half integral weight modular form. In this case the L function does not posess an Euler product. Subconvexity bounds for half Integral weight modular forms
Nov. 19, 2013 3pm (MATH 350)	Algebraic Geometry Matthew Satriano (U. Michigan) X We will discuss a technique which allows one to approximate singular varieties by smooth spaces called stacks. As an application, we will address the following question, as well as some generalizations: given a linear action of a group G on complex n-space C^n, when is the quotient C^n/G a singular variety? We will also mention some applications to Hodge theory and to derived equivalences. Stacky Resolutions of Singularities Sponsored by the Meyer Fund
Nov. 19, 2013 3pm (MATH 220)	PDE/Analysis Ryan Rosenbaum X Weyl's law describes the asymptotic distribution of the eigenvalues of the Laplacian on a compact Riemann manifold M with Dirichlet boundary condition. In the case that M is a torus, this quickly reduces to the classical problem of counting lattice points in a ball. We will prove Weyl's law in this case using a trace formula argument which generalizes considerably. Time permitting, we will sketch the proof of Weyl's law in a more general setting. Weyl's law via trace formulas
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

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