# Calendar

## Yesterday

### Department of Mathematics Colloquium, Jonathan Rosenberg, University of Maryland, MATH 175

Tuesday, October 21, 2014, 4:30 - 5:30 PM EDT

## Dualities in String Theory and the Baum-Connes Conjecture

Abstract: An amazing discovery of physicists is that there are many seemingly quite different physical quantum field theories that lead to the same observable predictions. Such theories are said to be related by dualities. A duality leads to interesting mathematical consequences; for example, certain K-theory groups on the two spacetime manifolds have to be isomorphic. We will explain how some of these K-theory isomorphisms predicted by physics correspond to certain cases of the Baum-Connes Conjecture, which originally was introduced for totally different reasons. Refreshments will be served in the Math Library Lounge at 4:00 p.m.### NSF GRFP Mathematical Sciences Prep Workshop, Professor Edray Goins, UNIV 103

Tuesday, October 21, 2014, 6:30 - 8:00 PM EDT

ABSTRACT: The National Science Foundation (NSF) Graduate Research Fellowship Program (GRFP) is perhaps this most prestigious graduate fellowship for those of us in the mathematical sciences. In this 90-minute workshop, we’ll discuss the specifics of the fellowship; the "do’s and don’ts” of applying for the fellowship; and best practices for maximizing your chances of being awarded the fellowship. At the workshop, we will have several Purdue staff and students in Mathematics and Statistics who have served on NSF GRFP panels and/or been awarded the fellowships over the years. If you have a partially completed fellowship which you wish to be read, feel free to bring your documents! Pizza will be at the session as well.

## Today

### Topology Seminar, Sean Tilson, University of Osnabrueck, BRNG B206

Wednesday, October 22, 2014, 1:30 - 2:30 PM EDT

## Power operations and Commutative ring spectra

Abstract: Power operations have been constructed and successfully utilized in a variety of spectral sequences. Such constructions arise from highly structured ring spectra. In this talk, we show that the Kunneth Spectral Sequence enjoys some nice multiplicative properties and use old computations of Steinberger's with our current work to compute operations in the homotopy of some relative smash products. We will then interpret these computations in terms of different commutative algebra structures. If time permits, we will mention ongoing work that interprets relative smash products in terms of Tannakian formalism.### Commutative Algebra Seminar, Professor Claudia Polini, University of Notre Dame, UNIV 119

Wednesday, October 22, 2014, 2:30 - 3:30 PM EDT

## Distance, Integral Dependence, and Associated Graded Rings

## Tomorrow

### Student Commutative Algebra Seminar, Jacob Boswell, Purdue University, BRNG B202

Thursday, October 23, 2014, 1:30 - 2:30 PM EDT

## Free Resolutions and Hilbert Functions, Part 8

### Representation Theory Seminar, Professor Bryden Cais, University of Arizona, UNIV 103

Thursday, October 23, 2014, 1:30 - 2:30 PM EDT

## Ramification in crystalline p-adic Galois representations

ABSTRACT: For a prime p and an abelian scheme A over the ring of integers O_K in a number field K, the p-adic Tate module V_pA provides a continuous linear representation \rho_A of the absolute Galois group G_K with coefficients in the field Q_p of p-adic numbers. This representation encodes a lot of the geometry and arithmetic of A, and is of serious interest in number theory. As G_K is (topologically) generated by decomposition subgroups {D_q} for q ranging over the primes of O_K, it is natural to study the restriction of \rho_A to each D_q. If q does not divide p, then this restriction is unramified, so is determined by a single matrix (the value on a Frobenius element). However, when q lies over p, the restriction of \rho_A to D_q is always deeply ramified (the image of the wild inertia subgroup is infinite), and it is natural to try and understand the nature of this wild ramification. In this talk, we will generalize a theorem of Kisin (independently proved by Beilinson and first conjectured by Breuil) which says, in a way that will be made precise, that crystalline p-adic representations (of which the restriction of \rho_A to D_q for q lying over p is an example) nonetheless behave a lot like unramified representations. This is joint work with Tong Liu.### PDE Seminar, Professor Patricia Bauman, Purdue University, REC 317

Thursday, October 23, 2014, 3:30 - 4:30 PM EDT

## Energy minimizers for a nonconvex variational problem

### Probability Seminar, Sveinn Olafsson, Purdue University, UNIV 103

Thursday, October 23, 2014, 3:30 - 4:30 PM EDT

## Short-time expansions for close-to-the-money options under a L\'evy jump model with stochastic volatility

Abstract: Due to their importance for model calibration and testing in financial engineering, small-time asymptotics for option prices have received considerable attention in recent years. Probabilistically, an option price can be expressed as the expectation of a r.v. of the form $\max\{\exp(X_{t})-K,0\}$, for a process $X=\{X_{t}\}_{t\geq{}0}$ and constant $K$, called the strike. In recent work, a small-time second order approximation for ATM option prices (i.e., when $K=0$) was developed for a large class of L\'evy processes $X$, with or without a Brownian component. In the present work we relax the imposed regularity conditions to what are arguably the minimal conditions for such an expansion to be well defined. Our approach is based on a suitable change of probability measure and on approximating the option price by the option prices of processes satisfying the more stringent regularity conditions. We also show that the formulas extend both to the case of ``close-to-the-money'' strikes (i.e., when $K=K_{t}\to{}0$ as $t\to{}0$) and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage effect. Another quantity of interest is the so-called ATM slope of the corresponding implied volatility curve, which can be expressed in terms of $\bbp(X_t\geq 0)$, the probability of the underlying process $X$ being positive at time $t$. By investigating the asymptotic behavior of this probability as $t\to{}0$, we also obtain an expansion for the ATM strike derivative as maturity tends to zero. This is joint work with Prof. Figueroa-L\'opez.## Friday

### Secret Seminar, Jacob Noparstak, Purdue University, UNIV 301

Friday, October 24, 2014, 11:30 - 12:30 PM EDT

## Compactification of Teichmüller space

Abstract: In this talk we will define three different approaches to finding compactifications of Teichmüller space. First, we will look at Thurston's classical approach, then a modern approach as seen in the work of Mondello, Liu, and many others. The final approach, which is very different, is due to Penner. This is a sequel to the talk on October 10, 2014## Next Week

### Computational & Applied Mathematics Seminar, Dr. Wujun Zhang, University of Maryland, REC 122

Monday, October 27, 2014, 3:30 - 4:30 PM EDT

## Discrete ABP Estimate and Rates of Convergence of Linear Elliptic PDEs in non-Divergence Form

Abstract: We design a finite element method (FEM) for linear elliptic equations in non-divergence form, which hinges on an integro-differential approximation of the PDE. We show the FEM satisfies the discrete maximum principle (DMP) provided that the mesh is weakly acute. Thanks to the DMP and consistency property of the FEM, we establish convergence of the numerical solution to the viscosity solution. We derive a discrete Alexandroff-Bakelman-Pucci (ABP) estimate for finite element methods. Its proof relies on a geometric interpretation of Alexandroff estimate and control of the measure of the sub-differential of piecewise linear functions in terms of jumps, and thus of the discrete PDE. The discrete ABP estimate leads to optimal rates of convergence for the finite element method under suitable regularity assumptions on the solution and coefficient matrix.### Department of Mathematics Colloquium, Francis Bonahon, University of Southern California, MATH 175

Tuesday, October 28, 2014, 4:30 - 5:30 PM EDT

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Student Commutative Algebra Seminar, Matthew Toeniskoetter, Purdue University, BRNG B202

Thursday, October 30, 2014, 1:30 - 2:30 PM EDT

## Free Resolutions and Hilbert Functions, Part 9

### Number Theory Seminar, Mr. Jeremy Fuller, Purdue University, MATH 731

Thursday, October 30, 2014, 3:30 - 4:30 PM EDT

## Genus Theory for Quadratic Forms Revisited: The Genus Field

Abstract: We discuss Section 6 of David Cox's book ``Primes of the Form $x^2 + n y^2$''.### Algebraic Geometry Seminar, Professor Mihai Fulger, Princeton University, MATH 731

Thursday, October 30, 2014, 3:30 - 4:30 PM EDT

## Positivity for Higher (co)dimensional Numerical Cycle Classes

Abstract: It is classical to study the geometry of a projective variety through positive cones of numerical classes of divisors or curves. The Mori cone in particular plays an important role in the classification of projective algebric varieties. A number of pathological examples have shifted attention from the higher (co)dimensional case. They show that the analogous definitions do not lead to the same positivity properties. To correct the negative outlook, I look at stronger positivity conditions. A sample result is that the pseudoeffective cone of numerical k-dimensional cycle classes is pointed for all k. The proof works in all characteristics, and without restrictions on singularities. This is in joint work with Brian Lehmann.### CCAM Lunch Seminar, Professor Zhilan Feng , Purdue University, REC 121

Friday, October 31, 2014, 11:30 - 12:30 PM EDT

TBA

## Two Weeks

### Computational & Applied Mathematics Seminar, Professor Jingfang Huang, University of North Carolina, Chapel Hill, REC 122

Monday, November 3, 2014, 3:30 - 4:30 PM EST

TBA

### Department of Mathematics Colloquium, Jean Bellissard, Georgia Tech, MATH 175

Tuesday, November 4, 2014, 4:30 - 5:30 PM EST

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Probability Seminar, Camelia Pop, University of Pennsylvania, UNIV 103

Thursday, November 6, 2014, 3:30 - 4:30 PM EST

### CCAM Lunch Seminar, Professor Guang Lin, Purdue University, REC 121

Friday, November 7, 2014, 11:30 - 12:30 PM EST

TBA

## Three Weeks

### Computational & Applied Mathematics Seminar, Professor Yuanwei Qi, University of Central Florida, REC 122

Monday, November 10, 2014, 3:30 - 4:30 PM EST

## Existence and Non-Existence of Traveling Waves in Isothermal Chemical Reaction Systems

Abstract: Traveling waves arises in many important physics and biology models. They play an important role in explaining many interesting biological phenomena. In this talk I shall present some recent results on the existence and non-existence of traveling waves for a class of chemical reaction systems.### Department of Mathematics Colloquium, Justin Moore, Cornell, MATH 175

Tuesday, November 11, 2014, 4:30 - 5:30 PM EST

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Probability Seminar, Daniel Kelleher, Purdue University, UNIV 103

Thursday, November 13, 2014, 3:30 - 4:30 PM EST

## November

### Department of Mathematics Colloquium, Boris Tsygan, Northwestern University, MATH 175

Tuesday, November 18, 2014, 4:30 - 5:30 PM EST

## TBA

Refreshments will be served in the Math Library Lounge at 4:00 p.m.### Probability Seminar, Anirban DasGupta, Purdue University, UNIV 103

Thursday, November 20, 2014, 3:30 - 4:30 PM EST

## Asymptotic Expansions Related to Ramanujam's First Letter to Hardy, the Rubin Conjecture, and their Poisson-Gamma Consequences

### Computational & Applied Mathematics Seminar, Professor Christopher Kribs, University of Texas at Arlington, REC 103

Thursday, November 20, 2014, 3:30 - 4:30 PM EST

TBA

Epistemic Uncertainty Quantification in Scientific Committee: Xiu (Co-Chair), Dong (Co-Chair), Buzzard, Li

### CCAM Lunch Seminar, Mr. Drew Swartz, Purdue University, REC 121

Friday, November 21, 2014, 11:30 - 12:30 PM EST

TBA

### Computational & Applied Mathematics Seminar, Professor Xu Yang, UC at Santa Barbara, REC 122

Monday, November 24, 2014, 3:30 - 4:30 PM EST

## Frozen Gaussian approximation and its applications

Abstract: We propose the frozen Gaussian approximation for the computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool based on the asymptotic analysis on phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam method, it overcomes the drawback of beam spreading. We will present numerical examples as well as preliminary application in seismology to show the performance of this method.### Computational & Applied Mathematics Seminar, Professor Jinglai Li, Shanghai Jiaotong University, REC 122

Monday, November 24, 2014, 4:30 - 5:30 PM EST

TBA

## December

### Computational & Applied Mathematics Seminar, Dr. Qifeng Liao, MIT, REC 122

Monday, December 1, 2014, 3:30 - 4:30 PM EST

## Reduced Order Modeling and Domain Decomposition Methods for Uncertainty Quantification

Abstract: Traditionally, terms in PDEs such as permeabilities, viscosities or boundary conditions have been treated as known deterministic quantities. However, these quantities are not always known with certainty, and there is much interest today in treating them as random fields. In this talk, I will present a reduced basis collocation method for efficiently solving PDEs with random coefficients, which is joint work with Howard Elman of University of Maryland. I will also present a domain-decomposed uncertainty quantification approach for complex systems, which is joint work with Karen Willcox of Massachusetts Institute of Technology.### CCAM Lunch Seminar, Professor Changyou Wang, Purdue University, REC 121

Friday, December 5, 2014, 11:30 - 12:30 PM EST

TBA