# Calendar

## Yesterday

### Mathematical Physics Seminar, Professor Laura Schaposnik, UIC Chicago, HAAS 101

Thursday, Jan 19 1:30 pm - 2:30 pm

## On Branes in the Moduli Space of Higgs Bundle

Abstract: The moduli space of Higgs bundles, as introduced by Hitchin in 1987, carries a natural Hyperkhaler structure through which one may consider A-branes (Lagrangian subspaces) and B-branes (holomorphic subspaces). During this talk, we shall first introduce Higgs bundles and the associated Hitchin fibration, and then describe different methods through which interesting branes may be constructed. Finally, we shall consider the geometry of these branes, and their relation to 3-manifolds, representation theory, and the geometric Langlands program.### Automorphic Forms and Representation Theory Seminar, Dr. Yong Suk Moon, Purdue University, WTHR 360

Thursday, Jan 19 1:30 pm - 2:30 pm

## Relative Crystalline Representations in the Unramified Case

Abstract: In this talk, we will study the integral structure of relative crystalline representations in the unramified case, using the relative generalization of Fontaine-Laffaille theory. As an application, we will see that when r < p-1, the locus of crystalline representations whose Hodge-Tate weights lie in [0, r] cuts out a closed subspace of the universal deformation ring.### PDE Seminar, Onur Alper, Courant Institute of Mathematical Sciences, REC 317

Thursday, Jan 19 3:30 pm - 4:30 pm

## Liquid Crystals with Variable Degree of Orientation

Abstract: We will discuss a modified Ericksen model for nematic liquid crystals with variable degree of orientation. In particular, we will address the structure of defects in minimizing configurations, focusing on the joint work with R. Hardt and F.H. Lin. We will also emphasize connections with harmonic maps into other cones, e.g. maps into trees, Q-valued maps, and touch upon the open question of rectifiability for defects, in the light of recent advances in harmonic map and nodal set theories.## Next Week

### Commutative Algebra Student Seminar, Mr. Monte Cooper, Purdue University, UNIV 119

Monday, Jan 23 3:30 pm - 4:30 pm

## Grobner Bases

### CCAM Seminar, Professor Howard Elman, University of Maryland, BRNG 1230

Monday, Jan 23 4:30 pm - 5:30 pm

## Efficient Computational Methods for Parameter-Dependent Partial Differential Equations

Abstract: We discuss efficient numerical algorithms for solving parameterized partial differential equations. These include reduced-basis methods, in which parameterized approximate solutions are constructed from a space of dimension significantly smaller than the dimension of the spatial discretization; stochastic Galerkin methods, in which a large deterministic solution is specified to produce approximate solutions that are easily evaluated; and stochastic collocation methods, in which approximation based on interpolation using so-called sparse grid methods. We outline the properties and costs of these methods, compare their performance on benchmark problems, and describe more specialized techniques needed when the underlying operator is nonlinear### Bridge to Research Seminar, Proessor Jeremy Miller, Purdue University, UNIV 103

Monday, Jan 23 4:30 pm - 5:30 pm

## Abelianizations of Some Groups

Abstract: Group homology is a generalization of the abelianization of a group. I will sketch a definition of group homology and describe homological stability. Then I will illustrate homological stability by computing the abelianization of symmetric groups, general linear groups, and braid groups.### Rigid Analytic Space and Berkovich Space Seminar, Mr. Heng Du, MATH 731

Tuesday, Jan 24 1:30 pm - 2:30 pm

## Introduction to Affinoid Algebras

Abstract: In this talk, we will study a number of properties of the Tate algebras T^n(K) and their quotient algebras. They play a role in rigid geometry much as the theory of polynomial rings over fields and their quotients in classical algebraic geometry.### Probability Seminar, Professor Rodrigo Bañuelos, Purdue University, REC 315

Tuesday, Jan 24 3:30 pm - 4:30 pm

## Littlewood-Paley Estimates for Lévy Processes

Abstract: The LpLp boundedness of certain Littlewood-Paley functionals that arise from Lévy processes are investigated. These results are applied to a new class of Fourier multiples which give LpLp bounds of solutions to non-local operators, including the fractional Laplacian. The latter has been extensively studied in recent years by researchers in analysis, probability and PDE.### Department of Mathematics Colloquium, Professor Michel Coste, Institut de Recherche Mathematique de Rennes, Universite de Rennes I, MATH 175

Tuesday, Jan 24 4:30 pm - 5:30 pm

## Nash Functions and Real Spectrum

Abstract: Zariski topology is too coarse to allow for an inverse function theorem in algebraic geometry. Étale topology is a way to recover such a theorem - but it is not a topology in the usual sense. It turns out that the real Étale topology (when one pays only attention to real points) actually yields a topological space, the real spectrum, which can be defined for any commutative ring (or any scheme). This space comes equipped with a sheaf of functions which are the Nash (= analytic-algebraic) functions, in the case of a smooth real variety. This sheaf of Nash functions on the real spectrum has bad cohomological properties. Nevertheless one has a satisfactory theory of finite Nash sheaves. One key step in the development of this theory is an application of an approximation theorem in commutative algebra known as general Néron desingularization.Refreshments will be served in the Math Library Lounge at 4:00 p.m

### Student Colloquium, Mr. Jacob Shapiro, Purdue University, UNIV 103

Wednesday, Jan 25 4:30 pm - 5:30 pm

## Exploring mathematical opportunities in industry: Math-to-Industry Boot Camp II

Abstract: Are you interested in mathematical opportunities outside academia? Are you curious to know how your math skills can be put to good use in industry or government? If so, then the Math-to-Industry Boot Camp II may be the right opportunity for you. This is an NSF funded workshop taking place this summer at the Institute for Mathematics and its Applications at the University of Minnesota. The workshop features coursework in programming and data analysis, interaction with mathematicians from industry, and two group projects. I will share my experience from the inaugural Boot Camp this past summer, as well as the results of the finance project that I worked on along with four grad students.### Real Algebraic Geometry Seminar, Marie-Françoise Roy, Universite de Rennes 1, REC 103

Thursday, Jan 26 11:00 am - 12:00 pm

## Elementary Recursive Quantifier Elimination Based on Thom Encoding and Sign Determination

Abstract: We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In particular, the notion of connected components of semialgebraic sets is not used.### Automorphic Forms and Representation Theory Seminar, Ms. Olivia Beckwith, Emory University, WTHR 360

Thursday, Jan 26 1:30 pm - 2:30 pm

## Indivisibility of Class Numbers of Imaginary Quadratic Fields

Abstract: I quantify a recent theorem of Wiles by proving an estimate for the number of negative fundamental discriminants down to -X whose class numbers are indivisible by a give prime and whose imaginary quadratic fields satisfy almost any given finite set of local conditions. This estimate matches the best results in the direction of the Cohen-Lenstra heuristics for the number of imaginary quadratic fields with class number indivisible by a given prime. I will also show how this result can be applied to study rank 0 twists of certain elliptic curves.### Operator Algebras Seminar, Professor Yasuhiko Sato, Kyoto University, REC 317

Thursday, Jan 26 2:30 pm - 3:30 pm

## Bogoiubov Actions of Amenable Groups on the CAR Algebra

Abstract: The canonical anti-commutation relation (CAR) is well-known to be based on the celebrated Pauli exclusion principle. For this reason, the CAR algebra is regarded as one of main examples in the study of C*-algebras. In a way parallel to the construction of the CAR algebra, the Bogoliubov actions can be defined. These actions are often applied to obtain unitary equivalence of quasi-free states and to diagonalize Hamiltonians. In this talk, starting with the basic study of the CAR algebra, I will explain about the classification theory on crossed products of Bogoliubov actions.### CCAM Lunch Seminar, Dr. Nam-Yong Lee, Inje University, Korea, REC 114

Friday, Jan 27 11:30 am - 12:30 pm

## Deconvolution Based Attenuation Correction and Image Reconstruction for Time-of-Flight Positron Emission

Abstract: The potential benefit of time-of-flight (TOF) information in positron emission tomography (PET) image reconstruction were studied in the early 1980s. However, the inefficiency of 1980s' scintillators has prevented TOF PET from becoming useful in clinical practices until the early 2000s. The introduction of new scintillators and continued improvements in the performance and reliability of photo-multiplier tubes (PMT) and electronics has reopened the interest of the research community in TOF PET.In PET, an accurate quantitative image reconstruction of annihilation positions requires taking into account the attenuation of the coincidence photons in the tissues. The research work in Defrise et al. shows that derivatives of the attenuation sinogram can be obtainable from derivatives of TOF data, without using any other transmission data such as those from CT scans.

In this talk, we propose a deconvolution based method for attenuation correction and image reconstruction. Through simulation, we will show that the ill-posedness of the numerical deconvolution based proposed method is less severe than that of the numerical differentiation based method in Defrise et al.

## Two Weeks

### CCAM Seminar, Professor Sara Pollock, Wright State University, BRNG 1230

Monday, Jan 30 4:30 pm - 5:30 pm

## TBA

### Probability Seminar, Professor Guang Lin, Purdue University, REC 315

Tuesday, Jan 31 3:30 pm - 4:30 pm

## Fast Numerical Methods for Solving Stochastic Differential Equations IA

Abstract: Stochastic differential equations arise in modeling of complex biological and environmental systems with uncertainties. Such uncertain sources could come from initial conditions, boundary conditions, forcing terms, and model parameters. Experience suggests that such uncertainties often play an important role in quantifying the performance of complex systems. Therefore, stochastic differential equations need to be treated as a core element in modeling, simulation and optimization of complex systems. The field of uncertainty quantification (UQ) by solving stochastic differential equations has received an increasing amount of attention recently. Extensive research efforts have been devoted to it and many novel numerical techniques have been developed. These techniques aim to solve stochastic differential equations. In this talk, I will present an efficient numerical method for solving stochastic differential equations - generalized polynomial chaos and some effective new ways of dealing with the discontinuities and high random dimensions. We will illustrate the main idea of our developed numerical algorithms for solving stochastic differential equations using groundwater flow in an aquifer problem.### Automorphic Forms and Representation Theory Seminar, Professor Dong Quan Ngoc Nguyen, Notre Dame University, WTHR 360

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

## TBA

## Three Weeks

### Probability Seminar, Professor Guang Lin, Purdue University, REC 315

Tuesday, Feb 7 3:30 pm - 4:30 pm

## Fast numerical methods for solving stochastic differential equations II

### Department of Mathematics Colloquium, Professor Xiang Tang, Washington University, Saint Louis, MATH 175

Tuesday, Feb 7 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 Jayce Getz, Duke University, WTHR 360

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

## TBA

### CCAM Lunch Seminar, Professor Sabre Kais, Purdue University, REC 114

Friday, Feb 10 11:30 am - 12:30 pm

## TBA

## February

### Department of Mathematics Colloquium, Thomas Koberda, University of Virginia, MATH 175

Tuesday, Feb 14 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 Naiomi Cameron, Lewis and Clark College, WTHR 360

Thursday, Feb 16 1:30 pm - 2:30 pm

## TBA

## TBA

### Department of Mathematics Colloquium, Professor Andrew Putman, University of Notre Dame, MATH 175

Tuesday, Feb 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 Joseph Hundley, University of Buffalo, WTHR 360

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

## TBA

### 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

## March

### Automorphic Forms and Representation Theory Seminar, Professor Martin Weissmann, UC Santa Cruz, WTHR 360

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

## TBA

### 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

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Department of Mathematics Colloquium, Christian Klingenberg, Wurzburg University, TBD

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

## TBA

### Automorphic Forms and Representation Theory Seminar, Professor Kelly McKinnie, University of Montana, WTHR 360

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

## TBA

### 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

## TBA

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, WTHR 360

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

## TBA

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

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m### 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