# Calendar

## Yesterday

### Commutative Algebra Seminar, Dr. Alessandro De Stefani, KTH, Stockholm, UNIV 219

Wednesday, Oct 26 1:30 pm - 2:30 pm

## Globalizing F-invariants

Abstract: The Hilbert-Kunz multiplicity and the F-signature are two important numerical invariants, defined for local rings of prime characteristic. They are subtly connected with the theory of singularities, and they often provide a good measure of how ill-behaved a ring can be. We will survey some classical results on these invariants. We will discuss how to extend these notions to rings that are not necessarily local in a way that still detects meaningful information about the ring. This is based on joint work with Thomas Polstra and Yongwei Yao.

### Informal Algebraic Geometry Seminar, Alex Barrios, Purdue University, REC 315

Wednesday, Oct 26 2:45 pm - 3:45 pm

## More on E'tale Maps

### Cookie Hour, MATH Library Lounge

Wednesday, Oct 26 3:15 pm - 3:45 pm

### Algebraic Geometry Seminar, Bo Lin, University of California, Berkeley, REC 315

Wednesday, Oct 26 3:45 pm - 4:45 pm

## Computing Linear Systems on Metric Graphs

Abstract: The linear system $|D|$ of a divisor $D$ on a metric graph has the structure of a cell complex. We introduce the anchor divisors and anchor cells in it - they serve as the landmarks for us to compute the f-vector of the complex and find all cells in the complex. A linear system can also be identified as a tropical convex set of rational functions. We compute its extremal generators using the landmarks. We apply these methods to some examples - namely the canonical linear systems of some small trivalent graphs. For the canonical linear system |K| on the complete graph $K_4$, we study the generic combinatorial type of |K| among the edge lengths in the orthant $\Bbb R^6_{>0}$.

### Student Colloquium, Mr. Nate Veldt, Purdue University, REC 307

Wednesday, Oct 26 4:30 pm - 5:30 pm

## Clustering in Low-Dimensions with Inconsistent Advice

Abstract: This talk provides an introduction to correlation clustering, a graph optimization problem for partitioning datasets based on potentially inconsistent "advice" about which objects are "similar" and which are "dissimilar." We'll start by using correlation clustering to solve the important problem of how to organize a seating arrangement at cookie hour to maximize the global happiness of people in the room. During the remainder of the talk we'll consider what happens when the advice can be stored as a low-rank matrix, and see a few interesting applications for this version of the problem.

## Today

### Automorphic Forms and Representation Theory Seminar, Professor Matthias Strauch, Indiana University, BRNG 1260

Thursday, Oct 27 1:30 pm - 2:20 pm

## Coverings of the p-adic Upper Half plane and Arithmetic Differential Operators

Abstract: The p-adic upper half plane comes equipped with a remarkable tower of GL(2)-equivariant etale covering spaces, as was shown by Drinfeld. It has been an open question for some time whether the spaces of global sections of the structure sheaf on such coverings provide admissible locally analytic representations. Using global methods and the p-adic Langlands correspondence for GL(2,Qp), this is now known to be the case by the work of Dospinescu and Le Bras. For the first layer of this tower Teitelbaum exhibited a nice formal model which we use to provide a local proof for the admissibility of the representation (when the base field is any finite extension of Qp). The other key ingredients are suitably defined sheaves of arithmetic differential operators and D-affinity results for formal models of the rigid analytic projective line, generalizing those of Christine Huyghe. This is joint work with Deepam Patel and Tobias Schmidt.

### Operator Algebras Seminar, Florin Boca, University of Illinois at Urbana-Champaign, MATH 731

Thursday, Oct 27 2:30 pm - 3:30 pm

## Distribution of Eigenvalues in Large Sieve Matrices

Abstract: The large sieve matrix provides an estimate for the largest eigenvalue of a certain N by N matrix A*A, where A is a Vandermonde type matrix defined by roots of unity of order at most Q. This talk will discuss some aspects concerning the behavior of the eigenvalues of these (large sieve) matrices when N ~ cQ^2, with Q-->\infty and c>0 constant. In particular, we will be interested in obtaining asymptotic formulas for their moments, and establish the existence of a limiting distribution as a function of c. This is joint work with Maksym Radziwill.

### Cookie Hour, MATH Library Lounge

Thursday, Oct 27 3:15 pm - 3:45 pm

### PDE Seminar, Professor Patrick Guidotti, University of California, Irvine, REC 303

Thursday, Oct 27 3:30 pm - 4:30 pm

## Domain Variations and Moving Boundary Problems

Abstract: Moving Boundary Problems are ubiquitous in applications and consist of (initial) boundary value problems for unknown quantities $u(t,\cdot)$ defined on evolving domains $\Omega(t)$ that are themselves an unknown of the problem. They are typically nonlinear in, at least, the unknown domain $\Omega$. Questions of, e.g., existence, regularity, and stability can often be analyzed via linearization. In this talk we propose a novel and more geometric approach to the computation of the relevant linearizations and a novel parametrization of the manifold of (limited smoothness) hypersurfaces in $\mathbb{R}^n$ which yields simpler and more transparent expressions of the linearizations.

### Real Algebraic Geometry Seminar, Antonio Lerario SISSA, Italy, REC 112

Thursday, Oct 27 4:30 pm - 5:30 pm

## Probabilistic Enumerative Geometry

Abstract: In this talk I will discuss a probabilistic approach Schubert Calculus (the computation of the cohomology ring of the Grassmannian). Over the complex numbers this leads to an alternative, more analytic, description of classical Schubert calculus, while over the reals it gives the average intersection theory of real random Schubert cycles. The talk will blend ideas from real algebraic geometry, integral geometry and random polytopes. (Joint work with P. Bürgisser)

## Tomorrow

### Commutative Algebra Seminar, Dr. Ali Alilooeedolatab, University of Wisconsin-Stout, UNIV 219

Friday, Oct 28 1:30 pm - 2:30 pm

## Regularity of Powers of Unicyclic Graphs

Abstract: The Castelnuovo-Mumford regularity is one of the most important invariants in commutative algebra. It has been investigated by various authors from different points of view. One of the interesting properties of regularity is its asymptotic behavior. In this talk, first we will see some well-known facts about regularity and then I will present some known results about the asymptotic behavior of quadratic square-free monomial ideals (edge ideals of graphs). At the end, my recent work with Selvi Beyarslan about regularity of unicyclic graphs will be presented.

### Cookie Hour, MATH Library Lounge

Friday, Oct 28 3:15 pm - 3:45 pm

## Next Week

### Cookie Hour, MATH Library Lounge

Monday, Oct 31 3:15 pm - 3:45 pm

### Bridge to Research Seminar, Prof. Edray Goins, Purdue University, UNIV 303

Monday, Oct 31 4:30 pm - 5:30 pm

## A Survey of Diophantine Equations

Abstract: There are many beautiful identities involving positive integers. For example, Pythagoras knew $3^2 + 4^2 = 5^2$ while Plato knew $3^3 + 4^3 + 5^3 = 6^3$. Euler discovered $59^4 + 158^4 = 133^4 + 134^4$, and even a famous story involving G.~H.~Hardy and Srinivasa Ramanujan involves $1^3 + 12^3 = 9^3 + 10^3$. But how does one find such identities? Around the third century, the Greek mathematician Diophantus of Alexandria introduced a systematic study of integer solutions to polynomial equations. In this talk, we'll focus on various types of so-called Diophantine Equations, discussing such topics as Pythagorean Triples, Pell's Equations, Elliptic Curves, and Fermat's Last Theorem.

### Advance Topic Exam (Yang Zhang), REC 307

Tuesday, Nov 1 3:00 pm - 4:30 pm

### Department of Mathematics Colloquium, Professor Andreas Seeger, University of Wisconsin, Madison, UNIV 317

Tuesday, Nov 1 3:30 pm - 4:30 pm

## The Haar System on Spaces of Sobolev Type

Abstract. It is well known that the system of Haar functions is an unconditional basis of $L^p(\Bbb R)$ for $1 < p < 1$. In the talk I will discuss what happens if $L^p$ is replaced by a Sobolev space $H^p_s$ .

Refreshments will be served in the Math Library Lounge at 3:00 p.m.

NOTE: DIFFERENT TIME AND LOCATION

### Cookie Hour, MATH Library Lounge

Wednesday, Nov 2 3:15 pm - 3:45 pm

### Algebraic Geometry Seminar, Greg Pearlstein, Texas A&M University, REC 315

Wednesday, Nov 2 3:45 pm - 4:45 pm

## Geometry of Nilpotent Cones in Hodge Theory

Abstract: The local monodromy of a degeneration of smooth complex projective varieties gives rise to a monodromy cone which plays a central role in constructing analogs of Mumford's toroidal compactifications for Hodge structures of arbitrary weight. In this talk, I will describe several methods for describing the possible monodromy cones which can arise in a given period domain using topological boundary components and signed Young diagrams.

### Student Colloquium, Mr. Daniel Slonim, Purdue University, REC 307

Wednesday, Nov 2 4:30 pm - 5:30 pm

## Path Sets and Interleaving

Abstract: I will first give a brief overview of how questions in number theory and fractal geometry led to a discussion of sequences generated by infinite walks on graphs. Given the right structure, a graph presents a set of sequences, called a "path set." We will look at interleaving and related operations on these path sets, discuss the effect these operations have on the graphs presenting the path sets, and discuss an algorithm for detecting path sets that are irreducible with respect to the interleaving operations. The algorithms I've come up with in the last year are extremely computationally expensive, even for small examples, and we will look at potential ways that they might be improved.

### Topology Seminar, Anibal Medina, Notre Dame, BRNG 2291

Wednesday, Nov 2 4:45 pm - 5:35 pm

## A Non-linear Dold-Kan Theorem and Algebraic Surgery

Abstract: The normalized chain functor, from simplicial sets to chain complexes of abelian groups, admits a factorization by the free functor to simplicial abelian groups followed by the Dold-Kan functor to chain complexes. The Dold-Kan Theorem states that this second functor is full and faithful. The first part of this talk will focus on the construction of a new factorization using a full-faithful functor and a forgetful one. The target of the first functor is the category of chain complexes enriched with an E-infinity coalgebra structure and we describe how to obtain such a structure from a finitely presented E-infinity prop. The second part of this talk will use the category of comodule over such coalgebras in the study of topological manifold structures on a given homotopy type.

### Automorphic Forms and Representation Theory Seminar, Dr. Hansheng Diao, Princeton University, BRNG 1260

Thursday, Nov 3 1:30 pm - 2:20 pm

## Log Adic Spaces and Overconvergent Modular Forms

Abstract: The main objects of the talk are adic spaces with logarithmic structures. In particular, we show that log adic spaces are locally "perfectoid". As an application, we establish an overconvergent Eichler-Shimura morphism connecting modular symbols and overconvergent modular forms. Same strategy also applies to Siegel case.

### Cookie Hour, MATH Library Lounge

Thursday, Nov 3 3:15 pm - 3:45 pm

### Real Algebraic Geometry Seminar, Sergei Starchenko, Notre Dame, REC 112

Thursday, Nov 3 4:30 pm - 5:30 pm

## An Elementary Proof of the Ax-Lindemann-Weierstrass Theorem for Abelian Varieties Over Complex Numbers

Abstract: In this talk I present a very elementary proof of the following theorem.

Theorem. Let $A$ be an abelian variety over $\mathbb{C}$ of dimension $g$, and $\pi\colon \mathbb{C}^g\to A$ be the uniformizing map. Let $V\subseteq \mathbb{C}^g$ be an irreducible algebraic variety. Then the Zariski closure of $\pi(V)$ is a translate of an abelian subvariety of $V$.

The proof uses ideal of Pila, Zannier, Ulmo, Yafaev and is based on basic properties of sets definable in o-minimal structures.

We will also discuss the case of semi-abelian varieties, and the real analytic case.

### Geometric Analysis Reading Seminar, Jacob Shapiro, Purdue University, MATH 731

Friday, Nov 4 10:00 am - 11:00 am

## Principles of Geometric Scattering Theory, Part I

Abstract: Scattering resonances play the role of eigenvalues for problems that take place on non-compact domains. We will illustrate the concept of resonances by investigating scattering by compactly supported perturbations of the Laplacian in one dimension. Then, we will discuss scattering resonances in higher dimensions and on certain classes of Riemannian manifolds. This material will prepare us for part two of the talk, in which we will apply the theory of resonances to establish local energy decay for the wave equation.

### Cookie Hour, MATH Library Lounge

Friday, Nov 4 3:15 pm - 3:45 pm

## Two Weeks

### Cookie Hour, MATH Library Lounge

Monday, Nov 7 3:15 pm - 3:45 pm

### CCAM Distinguished Seminar, Professor Roger Temam, Indiana University, LWSN 1142

Monday, Nov 7 4:30 pm - 5:30 pm

## Modeling Multiphase Problems of the Humid Atmosphere

Abstract: In this lecture, I will described some multiphase problems connected to the humid atmosphere. I will present the modeling of the problems, and the study of the existence, uniqueness and regularity of solutions to the problems. Because of the changes of phase , the governing equations appear to be nonlinear non continuous and non-monotone. In addition some unilateral effects, lead to the introduction of variational inequalities.

Refreshments will be served outside of LWSN 1142 from 4:00 PM until 4:30 PM.

### Cookie Hour, MATH Library Lounge

Tuesday, Nov 8 3:15 pm - 3:45 pm

### Cookie Hour, MATH Library Lounge

Wednesday, Nov 9 3:15 pm - 3:45 pm

### Algebraic Geometry Seminar, Colleen Robles, Duke University, REC 315

Wednesday, Nov 9 3:45 pm - 4:45 pm

## Characterization of Gross's Calabi-Yau Variations of Hodge Structure Type by Characteristic Forms

Abstract: Gross showed that to every Hermitian symmetric tube domain we may associate a canonical variation of Hodge structure (VHS) of Calabi-Yau type. The construction is representation theoretic, not geometric, in nature, and it is an open question to realize this abstract VHS as the variation induced by a family of polarized, algebraic Calabi-Yau manifolds.

In order for a geometric VHS to realize Gross's VHS it is necessary that the invariants associated to the two VHS coincide. For example, the Hodge numbers must agree. The later are discrete/integer invariants. Characteristic forms are differential-geometric invariants associated to VHS (introduced by Sheng and Zuo).

Remarkably, agreement of the characteristic forms is both necessary and sufficient for a geometric VHS to realize one of Gross's VHS. That is, the characteristic forms characterize Gross's Calabi-Yau VHS. I will explain this result, and discuss how characteristic forms have been used to study candidate geometric realizations of Gross's VHS.

### Cookie Hour, MATH Library Lounge

Thursday, Nov 10 3:15 pm - 3:45 pm

### CCAM Lunch Seminar, Yuanzhe Xi, University of Minnesota, REC 121

Friday, Nov 11 11:30 am - 12:30 pm

## TBA

### Cookie Hour, MATH Library Lounge

Friday, Nov 11 3:15 pm - 3:45 pm

## Three Weeks

### Cookie Hour, MATH Library Lounge

Monday, Nov 14 3:15 pm - 3:45 pm

### CCAM Distinguished Seminar, Bjorn Enquist , University of Texas at Austin, LWSN 1142

Monday, Nov 14 4:30 pm - 5:30 pm

## TBA

Refreshments will be served outside of LWSN 1142 from 4:00 PM until 4:30 PM.

### Jean Rubin Memorial Lecture, Gigliola Staffilani, MIT, MATH 175

Tuesday, Nov 15 4:30 pm - 5:30 pm

## TBA

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

### Spectral and Scattering Theory Seminar, Semyon Dyatlov, MIT, MATH 731

Wednesday, Nov 16 1:30 pm - 2:30 pm

## Dynamical Zeta Functions and Topology for Negatively Curved Surfaces

Abstract: For a negatively curved compact Riemannian manifold (or more generally, for an Anosov flow), the Ruelle zeta function is defined by $$\zeta(s)=\prod_\gamma (1-e^{-s\ell_\gamma} ),\quad \Re s\gg 1,$$ where the product is taken over all primitive closed geodesics $\gamma$ with $\ell_\gamma>0$ denoting their length. Remarkably, this zeta function continues meromorphically to all of $\mathbb C$.

Using recent advances in the study of resonances for Anosov flows and simple arguments from microlocal analysis, we prove that for an orientable negatively curved surface, the order of vanishing of $\zeta(s)$ at $s=0$ is given by the absolute value of the Euler characteristic. In constant curvature this follows from the Selberg trace formula and this is the first result of this kind for manifolds which are not locally symmetric. This talk is based on joint work with Maciej Zworski.

### Cookie Hour, MATH Library Lounge

Wednesday, Nov 16 3:15 pm - 3:45 pm

### Topology Seminar, Daniel Ramras, IUPUI, BRNG 2291

Wednesday, Nov 16 4:45 pm - 5:35 pm

## Coassembly for Representation Spaces

Abstract: I'll discuss models for a coassembly map from representation spaces to topological K-theory. At its most basic, this map carries a representation of G to the K-theory class of its associated vector bundle over BG. This map can be realized in at least two ways as a map of ring spectra, leading to various geometric consequences. In particular, I'll discuss applications to groups with property (T) and to flat connections over the 3-dimensional Heisenberg manifold.

### Automorphic Forms and Representation Theory Seminar, Professor Yifeng Liu, Northwestern University, BRNG 1260

Thursday, Nov 17 1:30 pm - 2:20 pm

## TBA

### Cookie Hour, MATH Library Lounge

Thursday, Nov 17 3:15 pm - 3:45 pm

### Number Theory Seminar, Mr. Tyler Billingsley, Purdue University, MATH 731

Thursday, Nov 17 4:30 pm - 5:30 pm

## Characters of $GL_n(\mathbb C)$

Abstract: We discuss Chapter 33 of Dan Bump’s Lie Groups (Second Edition).

### Cookie Hour, MATH Library Lounge

Friday, Nov 18 3:15 pm - 3:45 pm

## November

### Cookie Hour, MATH Library Lounge

Monday, Nov 21 3:15 pm - 3:45 pm

### Computational & Applied Mathematics Seminar, Professor Greg Beylkin, University of Colorado at Boulder, REC 114

Monday, Nov 21 4:30 pm - 5:30 pm

## TBA

### Graduate Student Invited Colloquium, Peter Sarnak, Princeton University, MATH 175

Tuesday, Nov 22 4:30 pm - 5:30 pm

## TBA

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

### THANKSGIVING BREAK, CLASSES ARE NOT IN SESSION

Wednesday, Nov 23 - Friday, Nov 25

### OFFICIAL UNIVERSITY HOLIDAY, ALL OFFICES ARE CLOSED IN OBSERVANCE OF THANKSGIVING

Thursday, Nov 24 - Friday, Nov 25

### Cookie Hour, MATH Library Lounge

Monday, Nov 28 3:15 pm - 3:45 pm

### Joint CS Colloquium and CCAM Seminar, Professor Jonathan Weare, University of Chicago, LWSN 3201A/B

Monday, Nov 28 3:30 pm - 4:30 pm

## TBA

### Department of Mathematics Colloquium, Professor Ragnar Buchweitz, University of Toronto, MATH 175

Tuesday, Nov 29 4:30 pm - 5:30 pm

## TBA

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

### Cookie Hour, MATH Library Lounge

Wednesday, Nov 30 3:15 pm - 3:45 pm

### Algebraic Geometry Seminar, Yuchen Liu, Princeton University, REC 315

Wednesday, Nov 30 3:45 pm - 4:45 pm

## Characterization of Projective Spaces by Seshadri Constants

Abstract: It is believed that the projective space has the most positive anti-canonical divisor among complex projective varieties. One way to measure the local positivity of a divisor is by using the Seshadri constant. We showed that an n-dimensional Fano variety with klt singularities is isomorphic to P^n if the Seshadri constant of its anti-canonical divisor at a smooth point is greater than n. This generalizes a result by Bauer and Szemberg where they showed for Fano manifolds. We also classify Fano varieties with Seshadri constants equal to n. This work is joint with Ziquan Zhuang.

## December

### Cookie Hour, MATH Library Lounge

Thursday, Dec 1 3:15 pm - 3:45 pm

### Number Theory Seminar, Mr. Abhishek Parab, Purdue University, MATH 731

Thursday, Dec 1 4:30 pm - 5:30 pm

## Duality Between $S_k$ and $GL_n (\Bbb C)$

Abstract: We discuss Chapter 34 of Dan Bump’s Lie Groups (Second Edition).

### CCAM Lunch Seminar, Ivan Christov, Purdue University, REC 121

Friday, Dec 2 11:30 am - 12:30 pm

## TBA

### Cookie Hour, MATH Library Lounge

Friday, Dec 2 3:15 pm - 3:45 pm

### Cookie Hour, MATH Library Lounge

Monday, Dec 5 3:15 pm - 3:45 pm

### CCAM Seminar, Professor He Yang, Ohio State University, REC 114

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

## TBA

### Cookie Hour, MATH Library Lounge

Wednesday, Dec 7 3:15 pm - 3:45 pm

### Automorphic Forms and Representation Theory Seminar, Dr. Bin Xu, University of Calgary, BRNG 1260

Thursday, Dec 8 1:30 pm - 2:20 pm

## TBA

### Cookie Hour, MATH Library Lounge

Thursday, Dec 8 3:15 pm - 3:45 pm

### Cookie Hour, MATH Library Lounge

Friday, Dec 9 3:15 pm - 3:45 pm

## 2017

### CCAM Seminar, Sara Pollock, Wright State University

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

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

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

### 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.

### Department of Mathematics Colloquium, Professor Andrew Putnam, 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.

### CCAM Seminar, Professor Christian Klingenberg, Wurzburg University, TBD

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

### 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, 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.

### CCAM Seminar, Professor Jan Hesthaven, Ecole Polytechnique Federale de Lausanne (EPFL)

Monday, Sep 11 4:30 pm - 5:30 pm