# Calendar

## Yesterday

### Commutative Algebra Seminar, Dr. Cory Colbert, Williams College, REC 303

Wednesday, Mar 29 1:30 pm - 2:30 pm

## Results concerning the spectrum of Noetherian rings

Abstract: A famous question of I. Kaplansky is "What partially ordered sets are order-isomorphic to the spectrum of some commutative Noetherian ring?" There have been many amazing results in this area, including R. Wiegand's classification of Spec(Z[x]), where x is an indeterminate over Z. We provide some partial results in the semilocal two-dimensional case, including a technique for "simplifying" partially ordered sets that might be useful in other cases. Time permitting, we will discuss cardinality restrictions that residue fields place on Noetherian spectra, and show a result about how much a ring can differ in cardinality from its spectrum### Spectral and Scattering Theory Seminar, Ting Zhou, Northeastern University, MATH 731

Wednesday, Mar 29 1:30 pm - 2:30 pm

## Nonparaxial near-nondiffracting accelerating optical beams

We show that new families of accelerating and almost nondiffracting beams (solutions) for Maxwell’s equations can be constructed. These are complex geometrical optics (CGO) solutions to Maxwell’s equations with nonlinear limiting Carleman weights. They have the form of wave packets that propagate along circular trajectories while almost preserving a transverse intensity profile. We also show similar waves constructed using the approach combining CGO solutions and the Kelvin transform.## An Introduction to Stacks

Abstract: A shortage of references, and long-winded definitions, can discourage geometry students from approaching this subject. The aim of this talk is to give a friendly introduction that emphasizes the need and utility of a stack.## Today

### Automorphic Forms and Representation Theory Seminar, Professor Shuichiro Takeda, University of Missouri, BRNG 1206

Thursday, Mar 30 10:30 am - 11:30 am

## The Langlands quotient theorem for symmetric spaces

Abstract: We will discuss how to generalize the Langlands quotient theorem to symmetric spaces. The key idea is to generalize so-called Casselman’s criterion for temperedness to the context of symmetric spaces by using the work of Kato-Takano.### Operator Algebras Seminar, Yunxiang Ren, Vanderbilt University, REC 317

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

## Classification of Thurston-relation planar algebra

Abstract: Planar algebras were introduced by Jones as a topological axiomatization of the standard invariants of subfactors. With this perspective, it is natural to understand subfactors through its skein theory, i.e, generators and relations (both algebraic and topological). In this talk, we will discuss the subfactor planar algebra generated by a 3-box with Thurston relation as a continuation of the classification program by skein theory proposed by Bisch and Jones. We give a full classification of such subfactors and explore these subfactors from its skein theory.### Topology seminar, Jennifer Wilson, Stanford University, BRNG 1243

Thursday, Mar 30 3:00 pm - 4:00 pm

## Stability in the second homology of Torelli groups

In this talk, I will describe stability results for two families of groups, the Torelli groups of automorphisms of free groups, and the Torelli groups of mapping class groups of surfaces with one boundary component. Specifically, I will explain the following statement: the degree-2 integer homology groups of these Torelli groups are centrally stable when viewed as representations of GLn(Z) and (respectively) Sp2n (Z). This project uses a framework developed by Putman, Church–Ellenberg–Farb, and Putman–Sam. This project is joint work with Jeremy Miller and Peter Patzt.### Joint topology and geometry seminar, Peter Patzt, Freie Universität Berlin, WTHR 160

Thursday, Mar 30 4:15 pm - 5:15 pm

## Representation stability for filtrations of Torelli groups.

We show, finitely generated rational VIC(Q)-modules and SI(Q)-modules are uniformly representation stable and all their submodules are finitely generated. We use this to prove two conjectures of Church and Farb, which state that the quotients of the lower central series of the Torelli subgroups of Aut(Fn) and Mod(Σg,1) are uniformly representation stable as sequences of representations of the general linear groups and the symplectic groups, respectively. Furthermore we prove an analogous statement for their Johnson filtrations## Tomorrow

## Randomized QR factorization with column pivoting

Abstract: Factorizing large matrices by QR with Column Pivoting (QRCP) typically requires substantially more processing time than QR without pivoting, owing to the communication costs required to process pivoting decisions. In contrast, randomized QRCP (RQRCP) algorithms have proven themselves empirically to be highly competitive with high-performance library implementations of QR in processing time, on uniprocessor and shared-memory machines, yet as reliable as QRCP in pivot quality. We show that RQRCP algorithms can be as reliable as QRCP with failure probability that exponentially decays with oversampling size. We investigate different updating formulas used in RQRCP and discuss the efficiency differences. We analyze the numerical stability of different RQRCP algorithms. Meanwhile, our distributed-memory implementation of RQRCP is significantly more efficient than the QRCP routines in ScaLAPACK.### Math 545 Harmonic Analysis Student Seminar, Seongmin Jeon, MATH 215

Friday, Mar 31 11:30 am - 12:30 pm

## Weak-type bounds for singular integrals and Riesz transform, Part I.

Abstract: Inspired in part by questions raised by E.M. Stein in his ICM 1986 Berkeley lecture, and in part by problems concerning singular integrals on infinite dimensions (Wiener space), the precise $L^p$ and weak-type norms of certain singular operators have been extensively studied for many year. While probabilistic techniques work extremely well to obtain sharp, or near sharp, $L^p$ bound for $1 \lt p \lt \infty$, they completely fail on $L^1$. In this talk we will present a modification of the celebrated Calderon-Zygmund decomposition and use it to show that for a large class of singular integrals with homogeneous kernels (including the Riesz transforms), the classical bounds from the Calderon-Zygmund theory can be improved from exponential growth to logarithmic growth with respect to dimension. The talk is based on work of Prabhu Janakiraman.## Next Week

### Math 545 Harmonic Analysis Student Seminar, Seongmin Jeon, MATH 215

Monday, Apr 3 11:30 am - 12:30 pm

## Weak-type bounds for singular integrals and Riesz transform, Part II.

Abstract: Inspired in part by questions raised by E.M. Stein in his ICM 1986 Berkeley lecture, and in part by problems concerning singular integrals on infinite dimensions (Wiener space), the precise $L^p$ and weak-type norms of certain singular operators have been extensively studied for many year. While probabilistic techniques work extremely well to obtain sharp, or near sharp, $L^p$ bound for $1 \lt p \lt \infty$, they completely fail on $L^1$. In this talk we will present a modification of the celebrated Calderon-Zygmund decomposition and use it to show that for a large class of singular integrals with homogeneous kernels (including the Riesz transforms), the classical bounds from the Calderon-Zygmund theory can be improved from exponential growth to logarithmic growth with respect to dimension. The talk is based on work of Prabhu Janakiraman.### Department of Mathematics Colloquium, Bruno Nachtergaele, University of California, Davis, BRNG 2291

Monday, Apr 3 2:30 pm - 3:30 pm

## The classification and stability of gapped phases of matter

Abstract: We will review recent results on the stability of gapped ground state phases and their classification. Here, stability refers to the robustness of qualitative properties against generic perturbations of moderate strength. These properties include the existence of a gap in the spectrum and the structure of elementary excitations above the ground state. We will illustrate the general results by considering the anyon sectors of Kitaev¹s quantum double models. Refreshments to be served from 2 pm - 2:30 pm in the Mathematics Lounge.### Theory Seminar, Koushik Ramachandran, Oklahoma State University, MATH 431

Monday, Apr 3 3:00 pm - 4:00 pm

## Equidistribution of zeros of random polynomials

Abstract: Consider a sequence of random polynomials $P_n(z) = \sum_{k=0}^{n}a_kB_k(z),$ where $\{a_k\}$ are i.i.d random variables and $B_k$ are deterministic polynomials selected from a standard basis such as Bergman or Szego polynomials associated to a Jordan domain $G$ with analytic boundary $E$. We show that the zero counting measures of $P_n$ converge almost surely to the equilibrium measure of the boundary $\mu_{E}$ if and only if $\mathbb{E}[\log^{+}|a_0|] < \infty.$ This talk is based on joint work with Igor Pritsker,### CCAM Distinguished Lecture Series, Professor John Ball, Oxford University, BRNG 1230

Monday, Apr 3 4:30 pm - 5:30 pm

## Some recent mathematical developments in liquid crystals

The understanding of liquid crystal behavior has traditionally been an area with a fertile interaction between science and mathematics. The lecture will describe different theories of liquid crystals and some recent results concerning their predictions and the connection between them Refreshments will be served outside of LWSN 1142 from 4:00 PM until 4:30 PM.### Department of Mathematics Colloquium, Tom Church, Stanford University, MATH 175

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

## Asymptotic representation theory over Z

Abstract: Representation theory over Z is famously intractable, but "representation stability" provides a way to get around these difficulties, at least asymptotically, by enlarging our groups until they behave more like commutative rings. Moreover, it turns out that important questions in topology / number theory / representation theory / ... correspond to asking whether familiar algebraic properties hold for these "rings". I'll explain how these connections work; describe what we know and don't know; and give a wide sampling of concrete applications in different fields. No knowledge of representation theory will be required -- indeed, that's sort of the whole point! Refreshments will be served in the MATH library lounge at 4:00 p.m.## Two Weeks

## 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.### Topology Seminar, Sam Nariman, Northwestern University, BRNG 1243

Thursday, Apr 13 3:00 pm - 4:00 pm

## Friedlander-Milnor's problem for diffeomorphism groups

Let G be a finite dimensional Lie group and G^delta be the same group with discrete topology. The natural homomorphism from G^delta to G induces a continuous map from BG^delta to BG. Milnor conjectured that this map induces a p-adic equivalence. In this talk, we discuss the same map for infinite dimensional Lie groups, in particular for diffeomorphism groups and symplectomorphisms. In these cases, we show that the map from BG^delta to BG induces split surjection on cohomology with finite coefficients in "the stable range". If time permits, I will discuss applications of these results in foliation theory, in particular flat surface bundles.### 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## Three Weeks

### 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

## April

### 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