# Calendar

## Yesterday

### Commutative Algebra Student Seminar, Mr. Michael Kaminski, Purdue University, UNIV 119

Monday, Feb 20 3:30 pm - 4:30 pm

## Simplicial Complexes and Alexander Duality

## Analysis and Numerical Methods for Fluid Flows in Poroelastic Media

Abstract: In this talk, we will introduce the Biot model for fluid flows in poroelastic media, which is coupling between the displacement of the poroelastic medium and the pressure of the fluid. In the model, the hydraulic conductivity is assumed to depend on the dilation of the medium, which makes the PDE system quasi-linear. We will discuss well-posedness, regularity, finite element approximations, and numerical experiments of the model problem.## Today

### Rigid Analytic Space and Berkovich Space Seminar, Chung Pang Mok , Purdue University, MA 731

Tuesday, Feb 21 1:30 pm - 2:30 pm

## Tate's acyclicity theorem

Abstract: We will discuss Cech cohomology of affinoid varieties and sketch the proof of Tate's acyclicity theorem.## Global rigidity of hyperbolic actions by higher rank lattices

Abstract: In this talk we will discuss a joint work with A. Brown and F. Rodriguez hertz on global rigidity of smooth Anosov actions by higher rank lattices on nilmanifolds. We show that if such an action lifts to the universal cover of the nilmanifold, then it is smoothly conjugate to an affine action. We will also discuss several assumptions that guarantees the lifting condition.## Particle representations for deterministic and stochastic reaction-diffusion equations

Abstract: Reaction diffusion equations (RDE) are an important and popular tool for modeling complex spatial-temporal patterns including Turing patterns, traveling waves and periodic switching. These models, however, ignore the stochasticity and discreteness of many complex systems in nature. Recognizing these discrepancies, scientists are developing individual-based models for model selection purposes. The latter models are sometimes studied under the framework of interacting particle systems (IPS) by mathematicians, who prove scaling limit theorems to connect various IPS with RDE. In this talk, I will present some new limiting objects including stochastic partial differential equations (SPDE) on metric graphs and coupled SPDE. These SPDE not only interpolate between IPS and RDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and novel duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of certain population dynamics. In particular, I will present rigorous results about the lineage dynamics of a biased voter model introduced by Hallatschek and Nelson (2007).### Department of Mathematics Colloquium, Professor Andrew Putman, University of Notre Dame, MATH 175

Tuesday, Feb 21 4:30 pm - 5:30 pm

## The high dimensional cohomology of the moduli space of curves with level structures

Abstract: I will prove that the moduli space of Riemann surfaces with level structures has a vast amount of rational cohomology in its cohomological dimension. No prior knowledge of the moduli space of curves will be assumed. This is joint work with Neil Fullarton. Refreshments will be served in the Math Library Lounge at 4:00 p.m.## Tomorrow

### Purdue University Numerical Linear Algebra Seminar, Nate Veldt, Purdue University, HEAV 102

Wednesday, Feb 22 12:00 pm - 1:00 pm

## Solving Low-Dimensional Optimization Problems via Zonotope Vertex Enumerati

Abstract: A zonotope is a centrally-symmetric convex polytope formed by projecting a high-dimensional hypercube into a lower-dimensional space. By using efficient procedures for zonotope vertex enumeration, a number of optimization problems that are typically NP-hard can be solved in polynomial time when the rank of the input matrix is a fixed constant. In this talk I will define and give examples of zonotopes, and demonstrate how they can be used to solve the binary quadratic maximization problem in polynomial time when the input matrix is low-rank. If time permits we will also consider how to solve the vector partition problem by enumerating vertices of the so-called signing zonotope.## The Orbit-Cone Correspondence

### Algebraic Geometry Seminar, Prakash Belkale, University of North Carolina, Chapel Hill, BRNG 1238

Wednesday, Feb 22 3:30 pm - 4:30 pm

## Topology of hyperplane arrangements and tensor product invariants, Part 1

Abstract: In the first part of this talk, we consider, in the context of an arbitrary hyperplane arrangement, the map between compactly supported cohomology to the usual cohomology of a local system. A formula (i.e., an explicit algebraic de Rham representative) for a generalized version of this map is obtained. These results are applied in the second part to invariant theory: Schechtman and Varchenko connect invariant theoretic objects to the cohomology of local systems on complements of hyperplane arrangements: To determine the image of invariants in cohomology. In suitable cases (e.g., corresponding to positive integral levels), the space of invariants is shown to acquire a mixed Hodge structure over a cyclotomic field. This is joint work with P. Brosnan and S. Mukhopadhyay.### Student Colloquium, Mr. Yingwei Wang, Purdue University, UNIV 103

Wednesday, Feb 22 4:30 pm - 5:30 pm

## The Electronic Schrodinger Equation

Abstract: The electronic Schrodinger equation plays a fundamental role in the theory of quantum mechanics and calculation of electronic structures, which in principle describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. In this talk, I will briefly review the physical background including many body quantum systems, the Born-Oppenheimer approximation, Kohn-Sham density functional theory, and the Pauli exclusion principle. In particular, I will focus on the mathematical results on the existence, regularity, and challenges in approximating the solutions of the electronic Schrodinger equation. Additionally, I will illustrate the idea of sparse grid methods and show how they can solve the electronic Schrodinger equation efficiently and accurately.## Thursday

### Automorphic Forms and Representation Theory Seminar, Professor Joseph Hundley, University of Buffalo, BRNG 1206

Thursday, Feb 23 10:30 am - 11:30 am

## On holomorphy of adjoint L-functions

Abstract: The adjoint $L$-function of an irreducible cuspidal automorphic representation $\pi$ of $GL_n(\A)$ ($\A$ the adeles of a number field), may be defined as $L(s, \pi, Ad) = L(s, \pi \times \tilde \pi)/\zeta(s),$ where $\tilde \pi$ is the contragredient. It is expected that this $L$ function is always entire. We discuss an approach to proving this in the special case $n=3,$ which is based on the integral representation for the partial adjoint L function due to Ginzburg. Our approach also applies to quasisplit unitary groups and to twisted adjoint L functions.### Algebraic Geometry Seminar, Prakash Belkale, University of North Carolina, Chapel Hill, MATH 731

Thursday, Feb 23 1:00 pm - 2:00 pm

## Topology of hyperplane arrangements and tensor product invariants, Part 2

This will be a continuation of the first talk on Wednesday, Feb. 22### Commutative Algebra Seminar, Professor Roger Wiegand, University of Nebraska, BRNG 2290

Thursday, Feb 23 1:30 pm - 2:30 pm

## Rigid Ideals in Complete Intersection Domains

An ideal J of R is said to be rigid provided every self-extension of J splits, that is, Ext^1_R(J,J) = 0. Suppose that R is a local Gorenstein domain of dimension one. In this context, there are no known examples of rigid ideals, except the obvious ones --- principal ideals. We conjecture, at least when R is a complete intersection domain of dimension one, that rigid ideals must be principal. This is closely related to a (still open) conjecture Huneke and I made in 1994: If M is a finitely generated module over a local domain (of any dimension), and if the tensor product of M with its dual is a maximal Cohen-Macaulay module, then M must be free. (An ideal J in a one-dimensional Gorenstein domain is rigid if and only if the tensor product of J with its dual is torsion-free.) In this talk I will give some positive results on complete intersections and also mention a family of examples (computer generated) where one might possibly look for counterexamples. This is a report on joint work with Craig Huneke and Srikanth Iyengar.## Cocycle superrigidity and group actions on C∗-algebras

Abstract: I will present the proof that any property (T) countable discrete group admits a continuum of pairwise non cocycle conjugate free actions on a UHF C*-algebra of infinite type. The main ingredient in the proof is Popa's cocycle superrigidity theory for noncommutative Bernoulli shifts. This is joint work with Eusebio Gardella.## Friday

### CCAM Lunch Seminar, Prof. Martin Bertodano, Purdue University, REC 114

Friday, Feb 24 11:30 am - 12:30 pm

## Shallow Water Theory Two-Fluid Model past the Kelvin-Helmholtz Instability

The four equations of the 1D Two-Fluid Model (TFM) are reduced to the two equations of Shallow Water Theory (SWT) using the fixed flux assumption. It is shown that this reduction introduces the Kelvin-Helmholtz instability (KH) into SWT. This in turn results in a fundamental difference in the behavior of the SWT equations and it makes them ill-posed. Fortunately adding a surface tension term restores well posed behavior. However the problem of exponential growth remains. This problem is addressed with viscosity. An experiment of the evolution of water-gasoline countercurrent KH waves in an inclined stratified channel is performed. The flow is laminar but the waves are strongly nonlinear. A 1D TFM simulation is used to study these waves. The simulations indicate that the flow becomes chaotic and that Lyapunov stability is attained.## Next Week

### Department of Mathematics Colloquium, Professor Kay Kirkpatric, University of Illinois at Urbana-Champaign, MATH 175

Tuesday, Feb 28 4:30 pm - 5:30 pm

## Bose-Einstein Condensation: from Many Quantum Particles to A Quantum "Superparticle"

Abstract: Near absolute zero, a gas of quantum particles can condense into an unusual state of matter, called Bose-Einstein condensation (BEC), that behaves like a giant quantum particle. We’ve made the rigorous connection between the physics of the microscopic many-body dynamics and the mathematics of the macroscopic model, the cubic nonlinear Schrodinger equation (NLS). I'll discuss recent progress on understanding fluctuations in quantum systems, and a couple of quantum central limit theorems. (Joint work with Gerard Ben Arous, Michael Brannan, Benjamin Schlein, and Gigliola Staffilani.)Refreshments will be served in the Math Library Lounge at 4:00 p.m

### Mathematical Physics, Prof. Kay Kirkpatrick, University of Illinois at Urbana-Champaign, HAAS 101

Wednesday, Mar 1 11:30 am - 12:30 pm

## Free Araki-Woods Factors and a Calculus for Moments in Quantum Groups.

Abstract: We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to almost-periodic free Araki-Woods factors. This is joint work with Michael Brannan.### Automorphic Forms and Representation Theory Seminar, Professor Martin Weissmann, UC Santa Cruz, WTHR 360

Thursday, Mar 2 1:30 pm - 2:30 pm

## TBA

### Topology seminar, Megan Maguire, University of Wisconsin, BRNG 1243

Thursday, Mar 2 3:00 pm - 4:00 pm

## Unstable cohomology of unordered configuration spaces

Abstract: In it's weakest form, we say that a family of topological spaces {X_n} is cohomologically stable if for fixed i the ith cohomology groups of X_n and X_{n+1} are isomorphic for n sufficiently large. Building off of results of Arnol'd, Segal, and McDuff, Church recently proved that the unordered configuration spaces of connected manifolds with finite cohomology are cohomologically stable if we take coefficients in Q. But what happens in the unstable cohomology? We will discuss stability phenomenon occurring in the unstable cohomology of configuration spaces of some manifolds, some of which we have proven and some of which we will give computational evidence for.## Two Weeks

### CCAM Seminar, Professor Christian Klingenberg, Wurzburg University, Germany, BRNG 1230

Monday, Mar 6 4:30 pm - 5:30 pm

## TBA

### Department of Mathematics Colloquium, Aaron Naber, Northwestern University, MATH 175

Tuesday, Mar 7 4:30 pm - 5:30 pm

## Energy Identity for Stationary Yang Mills

Abstract: Yang Mills connections over a principle bundle are critical points of the energy functional \int |F|^2, the L^2 norm of the curvature, and thus may be viewed as a solution to a nonlinear pde. In many problems, e.g. compactifications of moduli spaces, one considers sequences A_i of such connections which converge to a potentially singular limit connection A_i-> A . The convergence may not be smooth, and we can understand the blow up region by converging the energy measures |F_i|^2 dv_g -> |F|^2dv_g +\nu, where \nu=e(x)d\lambda^{n-4} is the n-4 rectifiable defect measure (e.g. think of \nu as being supported on an n-4 submanifold). It is this defect measure which explains the behavior of the blow up, and thus it is a classical problem to understand it. The main open problem on this front is to compute e(x) explicitly as the sum of the bubble energies which arise from blow ups at x, a formula known as the energy identity. This talk will primarily be spent explaining in detail the concepts above, with the last part focused on sketching a few details of the recent proof of the energy quantization, which is joint with Daniele Valtorta. The techniques may also be used to give the first apriori higher derivative estimates on Yang Mills connections, and we will discuss these results as well. Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Department of Mathematics Colloquium, Christian Klingenberg, Wurzburg University, BRNG 1245

Wednesday, Mar 8 4:30 pm - 5:30 pm

## TBA

No cookie hour today. Refreshments at 4 pm in the Library Lounge.### Automorphic Forms and Representation Theory Seminar, Professor Kelly McKinnie, University of Montana, WTHR 360

Thursday, Mar 9 1:30 pm - 2:30 pm

## Essential dimension of generic symbols in characteristic $p$

Abstract: The essential dimension of an algebraic object (think central simple algebra, quadratic form or a linear transformation) can be roughly defined as the minimum number of independent parameters needed to define the object. The essential dimension of an algebraic group is a numerical invariant of the group which can sometimes be identified with the minimum number of independent parameters needed to define all algebraic objects of a certain type. In this talk we will discuss how one can obtain lower bounds on the essential dimension of $\mathrm{ed}(\mathrm{PGL}_n)$ and $\math{ed}(\mathrm{GL}_n/\mu_m)$, especially in the case of bad characteristic.## March

### CCAM Seminar, Dr. John Glasser, The US Centers for Disease Control and Prevention, BRNG 1230

Monday, Mar 20 4:30 pm - 5:30 pm

## TBA

### Probability Seminar, Professor Jin Ma, University of South California, REC 315

Tuesday, Mar 21 3:30 pm - 4:30 pm

## TBA

### Department of Mathematics Colloquium, Professor Dietmar Bisch, Vanderbilt University, MATH 175

Tuesday, Mar 21 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Automorphic Forms and Representation Theory Seminar, Professor Taylor Dupuy, University of Vermont, WTHR 360

Thursday, Mar 23 1:30 pm - 2:30 pm

## TBA

### Department of Mathematics Colloquium, Dave Kung, St. Mary's College, Maryland, MATH 175

Tuesday, Mar 28 4:30 pm - 5:30 pm

## Theory & Practice: Mathematics and Music

Abstract: The two subjects of math and music are connected in myriad ways, from the rhythm of notes to the frequencies of the pitches. At the advanced level, both mathematical theories and music theories help us understand the other subject. In this talk, we first explore what mathematics tells us about musical instruments, the basic tools of musical practice. In the second half, we flip sides, looking at music theory and how the structure of chords gives us another way to understand topological structures (circles, Möbius strips and higher dimensional tori), some of the basic tools of mathematical practice. Thus the first half connects mathematical theory to musical practice, and the second connects musical theory to mathematical practice. Throughout, examples played on the violin will illustrate all of these beautiful and surprising connections. Refreshments will be served in the MATH library lounge at 4:00 p.m.### Automorphic Forms and Representation Theory Seminar, Professor Shuichiro Takeda, University of Missouri, BRNG 1206

Thursday, Mar 30 1:30 pm - 2:30 pm

## TBA

## April

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m### Department of Mathematics Colloquium, Tom Church, Stanford University, MATH 175

Tuesday, Apr 4 4:30 pm - 5:30 pm

## TBD

Refreshments will be served in the MATH library lounge at 4:00 p.m.### Automorphic Forms and Representation Theory Seminar, Dr. Kam Fai Tam, University of British Columbia, WTHR 360

Thursday, Apr 6 1:30 pm - 2:30 pm

## TBA

## Invisibility Cloaks: Mathematical and Numerical Analysis, and Simulation

Abstract: In the June 23, 2006's issue of Science magazine, Pendry et al and Leonhardt independently published their papers on electromagnetic cloaking. In Nov.10, 2006's Science magazine, Pendry et al demonstrated the first practical realization of such a cloak with the use of artificially constructed metamaterials. Since then, there is a growing interest in using metamaterials to design invisibility cloaks. In this talk, I will first give a brief introduction to invisibility cloaks with metamaterials, then I will focus on some time-domain cloaking models. Well-posedness study and time-domain finite element method for these models will be presented. Finally, I will show some numerical simulations of time-domain cloaking and optical black holes. I will conclude the talk with some open issues.### Department of Mathematics Colloquium, Professor Bill Velez, University of Arizona, MATH 175

Tuesday, Apr 11 4:30 pm - 5:30 pm

## The Central Role of a Mathematics Department in a University

Abstract: Change is in the air. The Common Vision project brought together leaders from five professional mathematical associations to collectively reconsider undergraduate curricula and ways to improve education in the mathematical sciences. In their report (http://www.maa.org/sites/default/files/pdf/CommonVisionFinal.pdf) they state, “A primary point emphasized ... is that the status quo is unacceptable. Change is unquestionably coming to lower-division undergraduate mathematics, and it is incumbent on the mathematical sciences community to ensure it is at the center of these changes, not on the periphery.” Providing relevant mathematical training should be at the core of a mathematics department, and in that role, it supports the goals of a university. If X is a major offered at the university, then double majoring in mathematics and X is a great combination. Adding the mathematics major to X provides unquestionable skills and makes X majors more competitive in the workforce and in pursuit of post-graduate education in X related fields. In 2003 I accepted the charge of directing the Math Center at the UA. I accepted it with one simple goal in mind. Every student at the UA should have mathematics as a major or a minor. I failed miserably in this goal but it did not dampen my enthusiasm or dedication to increasing the mathematical content of undergraduates’ course of study. In this talk I will describe my efforts to achieve this goal, how the mathematics department supports these efforts, and the institutionalization of some successful strategies.### Automorphic Forms and Representation Theory Seminar, Dr. Cris Negron, MIT, WTHR 360

Thursday, Apr 13 1:30 pm - 2:30 pm

## TBA

### Department of Mathematics Colloquium, Professor V. Kharlamov, University of Strasbourg, France , MATH 175

Thursday, Apr 13 4:30 pm - 5:30 pm

# Special date and time

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m### CCAM Seminar, Dr. Jorge Velasco-Hernandez, National University of Mexico, BRNG 1230

Monday, Apr 17 4:30 pm - 5:30 pm

## TBA

### Graduate Student Invited Colloquium, Robin Hartshorne, University of California, Berkeley, TBD

Tuesday, Apr 18 3:30 pm - 4:30 pm

## TBA

### Automorphic Forms and Representation Theory Seminar, Professor Michelle Manes, University of Hawaii, WTHR 360

Thursday, Apr 20 1:30 pm - 2:30 pm

## TBA

### CCAM Seminar, Dr. Michael Parks, Sandia National Laboratory, BRNG 1230

Monday, Apr 24 4:30 pm - 5:30 pm

## TBA

### Department of Mathematics Colloquium, Paul Bourgade, Courant Institute of Mathematical Sciences, New York University, MATH 175

Tuesday, Apr 25 4:30 pm - 5:30 pm

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Automorphic Forms and Representation Theory Seminar, Professor Jonathan Mboyo Esole, Northeastern University, WTHR 360

Thursday, Apr 27 1:30 pm - 2:30 pm

## TBA

## May

### Department of Mathematics Colloquium, Prof. Irene Fonseca, Carnegie Mellon University, TBD

Tuesday, May 9 4:30 pm - 5:30 pm