# Calendar

## Yesterday

### Commutative Algebra Student Seminar, Ms. Lindsey Hill, Purdue University, UNIV 119

Monday, Feb 27 3:30 pm - 4:30 pm

## Hilbert functions

### Geometry/Geometric Analysis Seminar, David Cohen, University of Chicago, MATH 731

Monday, Feb 27 3:30 pm - 4:30 pm

## Strongly aperiodic SFT on one-ended hyperbolic groups

Let G be a group and A a finite set. A subset X of A^G is said to be a subshift of finite type (SFT) if there is a finite set of "forbidden patterns" such that X consists of all points of A^G which in which these patterns never appear--for example, if X is the set of biinfinite words in the alphabet {0,1} such that no element of X contains 00 as a subword, then X is an SFT over the integers. A nonempty SFT is said to be strongly aperiodic if every point of X has trivial stabilizer in G. It is not hard to see that groups with at least two ends never admit strongly aperiodic SFTs, but many examples exist over one-ended groups. We will show that one-ended word hyperbolic groups always admit strongly aperiodic SFT. This is joint work with Chaim Goodman-Strauss and Yo'av Rieck.## Today

### Rigid Analytic Space and Berkovich Space Seminar, Prof. Chung Pang Mok, Purdue University, MATH 731

Tuesday, Feb 28 1:30 pm - 2:30 pm

## Tate's acyclicity theorem (II)

Abstract: The second part of last talk to prove Tate's acyclicity theorem via Cech cohomology of affinoid varieties.### 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

## Tomorrow

### Mathematical Physics Seminar, 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.## Nonsingular toric varieties

## Thursday

## Curvature of vector bundles associated to holomorphic fibrations

I will present a paper by Bo Berndtsson: Curvature of vector bundles associated to holomorphic fibrations. Consider a vector bundle whose fibers are weighted Bergman spaces, it is a trivial bundle with a nontrivial metric. We will show that if the weight function is plurisubharmonic, then this bundle is positive in the sense of Nakano. The needed inequality comes from L2-estimate. Moreover, I will discuss an analog of above theorem for holomorphic fibrations.### Automorphic Forms and Representation Theory Seminar, Professor Martin Weissmann, UC Santa Cruz, WTHR 360

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

## L-groups and Covering Groups

Abstract: To extend the Langlands program to covering groups, such as the metaplectic group, one needs to construct a dual group $G^\vee$ (a connected reductive group) and an L-group (an extension of the absolute Galois group, or Weil group, by $G^\vee$). In this talk I will introduce covering groups in a framework suggested by Brylinski and Deligne, and describe the construction of the dual group and L-group for such covering groups. To finish the talk, I will describe the current state of the art -- the evidence that this L-group is the "correct" choice, and some open questions.### Operator Algebras Seminar, Scott Atkinson, Vanderbilt University, REC 317

Thursday, Mar 2 2:30 pm - 3:30 pm

## Minimal faces and Schur’s Lemma for embeddings into R^U

As shown by N. Brown in 2011, for a separable II_1-factor N, the invariant Hom(N,R^U) given by unitary equivalence classes of embeddings of N into R^U--an ultrapower of the separable hyperfinite II_1-factor--takes on a convex structure. This provides a link between convex geometric notions and operator algebraic concepts; e.g. extreme points are precisely the embeddings with factorial relative commutant. The geometric nature of this invariant provides a familiar context in which natural curiosities become interesting new questions about the underlying operator algebras. For example, such a question is the following. "Can four extreme points have a planar convex hull?" The goal of this talk is to present a recent result generalizing the characterization of extreme points in this convex structure. After introducing this convex structure, we will see that the dimension of the minimal face containing an equivalence class [\pi] is one less than the dimension of the center of the relative commutant of \pi. This result also establishes the "convex independence" of extreme points, providing a negative answer to the above question. Along the way we make use of a version of Schur's Lemma for this context. No prior knowledge of this convex structure will be assumed.### 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.## Next Week

### Geometry/Geometric Analysis Seminar, Professor Nan Li, City University of New York, MATH 731

Monday, Mar 6 3:30 pm - 4:30 pm

## Quantitative Estimates on the Singular Sets of Alexandrov Spaces

The definition of quantitative singular sets was initiated by Cheeger and Naber. They proved some volume estimates on such singular sets in non-collapsed manifolds with lower Ricci curvature bounds and their limit spaces. On the quantitative singular sets in Alexandrov spaces, we obtain stronger estimates in a collapsing fashion. We also show that the (k,\epsilon)-singular sets are k-rectifiable and such a structure is sharp in some sense. This is a joint work with Aaron Naber.### CCAM Seminar, Professor Christian Klingenberg, Wurzburg University, Germany, BRNG 1230

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

## The compressible Euler equations with gravity: well-balanced schemes and all Mach number solvers

Abstract: We consider astrophysical systems that are modeled by the multidimensional Euler equations with gravity. First for the homogeneous Euler equations we look at flow in the low Mach number regime. Here for conventional finite volume discretizations one has excessive dissipation in this regime. We identify inconsistent scaling for low Mach numbers of the numerical fux function as the origin of this problem. Based on the Roe solver a technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations is proposed. We analyze properties of this scheme and demonstrate that its limit yields a discretization of the incompressible limit system. Next for the Euler equations with gravity we seek well-balanced methods. We describe a numerical discretization of the compressible Euler equations with a gravitational potential. A pertinent feature of the solutions to these inhomogeneous equations is the special case of stationary solutions with zero velocity, described by a nonlinear PDE, whose solutions are called hydrostatic equilibria. We present well-balanced methods, for which we can ensure robustness, accuracy and stability, since it satisfies discrete entropy inequalities. We will then present work in progress where we combine the two methods above.### 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

## The universe in a computer: how mathematical and numerical methods are essential.

We will talk about our contribution to a large project with the goal of a self-consistent numerical simulation of the evolution of the universe beginning soon after the Big Bang and ending with the formation of realistic stellar systems like the Milky Way. This is a multi-scale problem of vast proportions. It requires the development of new numerical methods that excel in accuracy, parallel scalability to the processes relevant in galaxy formation. These numerical methods themselves require the development of mathematical theory in order to guarantee the above mentioned requirements. in this talk we shall focus on our contribution to this effort. This is joint work among others with Volker Springel. 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.## Three Weeks

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

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

## Identifying Optimal Vaccination Strategies for Eliminating Measles and Controlling Rubella in China

In a series of articles, we have shown that the approach used by public health authorities worldwide to guide vaccination efforts is limited to homogeneous populations. And we have suggested an alternative that works in heterogeneous populations whose sub-populations differ in characteristics affecting their reproduction numbers (average number of secondary infections per infectious person) or whose constituents mix non-randomly. Our alternative is the multivariate partial derivative of the effective reproduction number, for which expressions can be derived from suitable transmission models, with respect to one of its parameters. As a proof of principle, we compared vaccination against pandemic H1N1 in the United States (the 50 states plus District of Columbia) by age (the 7 classes by which vaccination coverage was reported) and month (from October of 2009, when vaccine became available, through June of 2010) to the optimal strategy (for reducing the average number of secondary infections per infectious person). While the gradient is not new mathematics, it is cutting-edge public health. And, thanks largely to a colleague who is seconded to the WHO Office in Beijing, we are using it to guide measles elimination and rubella control in the largest and possibly most diverse population on earth.### 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

## March

### Function Theory Seminar, Michael Zieve, University of Michigan, BRNG 1243

Tuesday, Mar 28 3:00 pm - 4:00 pm

## Value sharing of meromorphic functions, and functional equations

Abstract: Let p,q be nonconstant meromorphic functions on the complex plane. Nevanlinna showed that if the preimages under p,q of five distinct points on the Riemann sphere are the same, then p=q. I will present a generalization of this result to preimages of finite sets, however under the more restrictive hypothesis that the preimages are the same counting multiplicities. The result says that if there are five pairwise disjoint nonempty finite subsets S_1,...,S_5 of the Riemann sphere such that, for each i, the p- and q- preimages of S_i counted with multiplicities are identical to one another, then there is a nonconstant rational function f such that f o p = f o q. I will also explain recent work which come close to describing all solutions of this functional equation.### 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