# Calendar

## Tomorrow

Refreshments served in the Library Lounge

### Student Commutative Algebra Seminar, Ms. Rachel Lynn, Purdue University, UNIV 103

Monday, Oct 23 3:30 pm - 4:20 pm

## Powers and Formal Equidimensionality

### Geometry/Geometric Analysis Seminar, Prof. Mark Lawrence, Nazarbayev University, Kazakhstan, and Stony Brook University, MATH 731

Monday, Oct 23 3:30 pm - 4:20 pm

## The 1-dimensional extension property in complex analysis

Abstract### (Special date) Operator Algebras Seminar, Daniel Drimbe, UC San Diego, MATH 731

Monday, Oct 23 4:30 pm - 5:20 pm

## Prime II_1 factors arising from irreducible lattices in products of rank one simple Lie groups

Abstract: In this talk I will present joint work with Daniel Hoff and Adrian Ioana in which we obtain that II_1 factors associated to icc irreducible lattices in products of simple Lie groups of rank one are prime, i.e. they cannot be decomposed as a tensor product of II_1 factors. This gives the first examples of prime II_1 factors arising from lattices in higher rank semisimple Lie groups.## An introduction to gravitational instantons

Abstract: Gravitational instantons are building blocks of canonical metrics on four manifolds. After giving the definition, I will discuss some examples and their roles in the convergence and gluing construction of canonical metrics.## Next Week

### Special Automorphic Forms and Representation Theory Seminar, Prof. Chandrasheel Bhagwat, IISER, BRNG 1260

Tuesday, Oct 24 1:30 pm - 2:20 pm

## TBA

Note the special date and time.Refreshments served in the Library Lounge prior to Colloquium.

### Department Colloquium, Prof. Alexei Pantchichkine, Institut Fourier - Université de Grenoble, MATH 175

Tuesday, Oct 24 3:30 pm - 4:20 pm

## Constructions of p-adic L-functions and admissible measures for Hermitian modular forms

Abstract: Methods of constructing $p$-adic L-functions are discussed, including $p$-adic version of Shahidi's method. A new striking analogy between elliptic and Hermitian modular cases is presented as follows. For a positive integer $n$, the standard zeta function $L_F(s)$ is considered, attached to an Hermitian modular form $F=\sum_H A(H) q^H$ on the Hermitian upper half plane $H_m$ of degree $n$, where $H$ runs through semi-integral positive definite Hermitian matrices of degree $n$. Analytic $p$-adic continuation of these $L$-functions is build from $p$-adic measures, bounded or growing. Main result is stated in terms of the Hodge/Newton polygons.### Spectral and Scattering Theory Seminar, David Borthwick, Emory University, MATH 731

Wednesday, Oct 25 1:30 pm - 2:20 pm

## Distribution of Resonances for Hyperbolic Surfaces

Abstract: For non-compact hyperbolic surfaces, the appropriate generalization of the eigenvalue spectrum is the resonance set, the set of poles of the resolvent of a meromoprhic continuation of the Laplacian. Hyperbolic surfaces serve as a model case for quantum theory when the underlying classical dynamics is chaotic. In this talk I’ll explain how the resonances are defined and discuss our current understanding of their distribution. I’ll introduce some conjectures inspired by the physics of quantum chaotic systems, and discuss numerical evidence for these conjectures and the partial progress that has been made recently.### Function Theory, Alastair Fletcher, Northern Illinois University, UNIV 317

Wednesday, Oct 25 1:30 pm - 2:20 pm

## Strongly automorphic mappings

A result of Ritt highlights the connection between periodic functions and certain rational maps: power of z, Chebyshev polynomials and Lattes rational maps. We will discuss the quasiregular counterparts of this relationship in higher dimensions, including: (i) constructions of strongly automorphic mappings, (ii) a classification in terms of crystallographic orbifolds for which automorphism groups give rise to such mappings, (iii) showing that solving the Schroeder functional equation yields a uniformly quasiregular map whose Julia set is either a quasi-sphere, quasi-disk or all of space, (iv) time allowing, we will discuss to what extent the converse can apply and a three dimensional Denjoy-Wolff Theorem. This is based on joint work with Doug Macclure (NIU).### Probability Seminar, Tal Orenshtein, UniversitŽ de Lyon 1, UNIV 101

Wednesday, Oct 25 1:30 pm - 2:20 pm

## Critical wetting models in (1+1) dimensions

In this talk we will discuss wetting models in (1+1) dimensions pinned to a shrinking strip. Except for the space geometry effect (the one dimensional lattice, in our case) these polymer models enjoy an interplay between two forces -- local (pinning) and global (entropic repulsion) -- and one expects a localization-delocalization phase transition to hold. When the strip size is fixed and the pinning function is constant and homogeneous, phase transition results are known, and moreover, the standard case (zero strip size) is completely solved and exhibits a sharp phase transition. In particular, the system behavior is drastically different in the three phases, sub-criticality, super criticality and criticality. We will focus on shrinking strips at criticality. Joint work in progress with Jean-Dominique Deuschel.## Higher G-torsion and polylogarithms

This is a report on joint work with Tom Goodwillie based on earlier joint work with Goodwillie and Ohrt. In this project we generalize a very elegant topological construction of Allen Hatcher to explicitly construct exotic smooth structures on smooth manifold $G$-bundles and compute their higher Franz-Reidemeister torsion invariants to verify that they are nonstandard. The talk will review the history, then give a brief description of the new construction and the linear independence properties of polylogarithms of roots of unity which imply the linear independence of the exotic equivariant bundles.Refreshments served in the Library Lounge

## 1-motives associated to degenerations of curves (cont.)

Abstract: We will give the Deligne 1-motives up to isogeny corresponding to the $\mathbb{Q}$-limiting mixed Hodge structures of semi-stable degenerations of curves, by using logarithmic structures and Steenbrink's cohomological mixed Hodge complexes associated to semi-stable degenerations of curves.## The Geometry of Surfaces

Abstract: Thurston revolutionized the field of $3$-manifolds with his Geometrization Conjecture which, roughly stated, says that a compact orientable $3$-manifold $M$ can be cut into disjoint embedded $2$-spheres and tori pieces such that, after gluing $3$-balls to all boundary spheres, he interior of said manifold admits one (and only one) of eight geometric structures with finite volume. In today's Student Colloquium, we discuss the situation for $2$-manifolds which, as you may already know, admit one of Euclidean, spherical, or hyperbolic structures; these are just three of the eight geometries we can place on a $3$-manifold, but hyperbolic already accounts for a majority of said structures. If time permits, we will say more about the Geometrization Conjecture, the proof of which was instrumental in solving the long-standing Poincaré Conjecture.### Commutative Algebra Seminar,Dr. Jack Jeffries, University of Michigan,REC 308

Thursday, Oct 26 1:30 pm - 2:20 pm

## A Zariski-Nagata theorem in mixed characteristic

Abstract: One version of a classical result by Zariski and Nagata describes symbolic powers in polynomial rings over the complex numbers in terms of differential operators. Namely, the n-th symbolic power of a prime consists of the elements such that each differential operator of order at most n-1 sends the element into the prime ideal. This was extended to polynomial rings over perfect fields by Dao, De Stefani, Grifo, Huneke, and Núñez-Betancourt. However, this description fails in mixed characteristic. In this paper, we use p-derivations, a notion due to Buium and Joyal, to define a new kind of differential powers in mixed characteristic, and prove that this new object does coincide with the symbolic powers of prime ideals. This is joint work with Alessandro De Stefani and Eloísa Grifo.Refreshments served in the Library Lounge

### Department of Statistics Research Colloquium, Philip Protter, Columbia University, GRIS 103

Friday, Oct 27 10:30 am - 11:30 am

## Issues of Incomplete Markets

Abstract: In a complete market, there is a unique risk neutral measure, unique prices, and all contingent claims can be (at least theoretically) perfectly hedged. In an incomplete market, in contrast, there is an infinite number of risk neutral measures, a continuum of “fair” prices, and contingent claims can in general not be perfectly hedged, even theoretically. Unfortunately, there seems to be plenty of evidence markets in actuality are incomplete. We are interested in trying to understand this a priori confusing situation. To make things concrete, we address the following question: Suppose a sequence of incomplete markets “converges” to a complete market in an appropriate sense (to be defined), do the major objects also converge? Mostly, this is false: the ranges of option prices do not converge, for example. We work out some simple examples that illustrate some of the issues, and we indicate when one might have some kind of reasonable convergence of the markets, and what such a convergence might be. The talk is back on joint work with Jean Jacod.### CCAM Lunch Seminar, Prof. Guang Cheng, Purdue University, LWSN B134

Friday, Oct 27 11:30 am - 12:20 pm

## Low Rank Tensor Recovery via Cubic Sketching

In this presentation, we propose a general framework for recovering sparse and low-rank tensors through rank-one cubic sketching. Two real-world applications are considered: one on high-dimensional interaction models; another on compressed image transmission. A block-wise thresholded gradient decent algorithm is proposed for stable recovery in both noiseless and noisy cases. Both upper bound and lower bounds for the estimation accuracy are obtained over a large class of low-rank tensors, demonstrating the optimality of the proposed procedure. This is an ongoing work with Botao Hao and Anru Zhang.Refreshments served in the Library Lounge

## Two Weeks

Refreshments served in the Library Lounge

### CCAM Seminar, Prof. Xiaochuan Cai , Univ. of Colorado at Boulder, UNIV 103

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

## TBD

Refreshments served in the Library Lounge prior to Colloquium.

### Department Colloquium, Prof. Craig Sutton, Dartmouth College, MATH 175

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

Refreshments served in the Library Lounge

### Automorphic Forms and Representation Theory Seminar, Prof. Francesc Castella, Princeton University, BRNG 1260

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

## Elliptic curves of rank two and generalized Kato classes

Abstract: The generalized Kato classes of Darmon-Rotger arise as p-adic limits of diagonal cycles on triple products of modular curves, and in some cases, they are predicted to have a bearing on the arithmetic of rational elliptic curves of rank two. In this talk, we will report on a joint work in progress with Ming-Lun Hsieh concerning a special case of the conjectures of Darmon-Rotger.Refreshments served in the Library Lounge

## Three Weeks

## Automated Modeling with FEniCS

The FEniCS Project develops both fundamental software components and end-user codes to automate numerical solution of partial differential equations (PDEs). FEniCS enables users to translate scientific models quickly into efficient finite element code and also offers powerful capabilities for more experienced programmers. FEniCS uses the variational formulation of PDEs as a language to define models. We will explain the variational formulations for simple problems and then show how they can be extended to simulate fluid flow. The variational formulation also provides a firm theoretical foundation for understanding PDEs. We argue that combining the theory with practical coding provides a way to teach PDEs and associated modeling without requiring extensive mathematical prerequisites. As proof, this talk will require no background in PDEs or finite elements, only multi-variate calculus.Refreshments served in the Library Lounge prior to Colloquium.

### Department Colloquium, Prof. Kasso Okoudjou, University of Maryland, MATH 175

Tuesday, Nov 7 3:30 pm - 4:20 pm

## TBA

## TBA

Refreshments served in the Library Lounge

### Automorphic Forms and Representation Theory Seminar, Prof. Shunsuke Yamana, Kyoto University, BRNG 1260

Thursday, Nov 9 1:30 pm - 2:20 pm

## Title: TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

## November

Refreshments served in the Library Lounge

## Blind deconvolution by Optimizing over a Quotient Manifold

Blind deconvolution is to recover two unknown signals from their convolution. We formulate this problem as a nonconvex optimization problem on a quotient manifold and propose Riemannian optimization algorithms for solving the problem. The proposed algorithm is proven to recover the exact solution with high probability when the number of measurements is (up to log-factors) slightly larger than the information-theoretical minimum, which is the same as the state-of-the-art results. The quotient structure in our formulation yields a simpler penalty term in the cost function when compared to the state-of-the-art nonconvex method. This simplifies the convergence analysis to some extent and yields a natural implementation. Empirically, the algorithm has the best performance in the sense that compared to state-of-the-art methods, i) it needs least number of various operations, such as DFT, to reach a similar accuracy, and ii) it has the highest probability of successful recovery. This is joint work with Paul Hand at Rice university.Refreshments served in the Library Lounge prior to Colloquium.

### Department Colloquium, Prof. Sandra Cerrai, University of Maryland, MATH 175

Tuesday, Nov 14 3:30 pm - 4:30 pm

## TBD

## TBA

Refreshments served in the Library Lounge

### Automorphic Forms and Representation Theory Seminar, Dr. Ozlem Edjer, Colorado State University, BRNG 1260

Thursday, Nov 16 1:30 pm - 2:20 pm

## Title: TBA

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge

## Transport for Seismic Inversion

Abstract: Optimal transport has become a well-developed topic in the analysis since it was first proposed by Monge in 1781. Due to their ability to incorporate differences in both intensity and spatial information, the related Wasserstein metrics have been adopted in a variety of applications, including seismic inversion. The quadratic Wasserstein metric ($W_2$) has ideal properties like convexity and insensitivity to noise, while conventional $L^2$ norm is known to suffer from local minima. We propose two ways of using W2 in seismic inversion, a trace-by-trace comparison solved by 1D exact formula, and the global comparison which requires the numerical solution of Monge-Ampère equation. The 1D approach has been successfully applied to field data in collaboration with PGS, Inc. I will discuss the connection between the Wasserstein metric $W_p$ and the Sobolev space $W^{-1,p}$. This is a joint work with Dr. Björn Engquist, Brittany Froese, Junzhe Sun and Lingyun Qiu.Refreshments served in the Library Lounge

### CCAM Seminar, Dr. Xiu Yang , Pacific Northwest National Lab, UNIV 103

Monday, Nov 27 4:30 pm - 5:20 pm

## Alternating direction method for enhancing sparsity of the representation of uncertainty

Abstract: Compressive sensing has become a powerful tool for uncertainty quantification when only limited data is available. We provide a general framework using alternating direction method to enhance the sparsity of the representation of uncertainty in the form of generalized polynomial chaos expansion. This method identifies new sets of random variables through iterative rotations such that the new representation of the uncertainty using these variables is sparser. Consequently, we increase both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. We demonstrate the effectiveness of this method with applications in analyzing uncertainties in high-dimensional complex systems.Refreshments served in the Library Lounge prior to Colloquium.

Refreshments served in the Library Lounge

### Automorphic Forms and Representation Theory Seminar, Prof. Aaron Pollack, Duke University, BRNG 1260

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

## Title: TBA

Refreshments served in the Library Lounge

## December

### CCAM Lunch Seminar, Prof. David Gleich, Purdue University, LWSN B134

Friday, Dec 1 11:30 am - 12:20 pm

## TBD

### CCAM Seminar, Prof. Padmanabhan Seshaiyer , National Science Foundation, UNIV 103

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

Refreshments served in the Library Lounge prior to Colloquium.

Refreshments served in the Library Lounge

Refreshments served in the Library Lounge