Departmental Colloquium 2017-2018

Thursdays, 4:00 PM, JWB 335

Fall 2017

August 31: AWM Colloquium
Speaker: Moon Duchin, Tufts University
Title: Can you hear the shape of a billiard table?
Abstract: There are many ways to associate a spectrum of numbers to a surface: two of the most classically studied are the eigenvalues of the Laplacian and the lengths of closed geodesics. People often ask whether two different surfaces can have the same spectrum of numbers, and there's a long and beautiful story attached to that question. Here's a twist on the setup: now consider a polygon in the plane, and label its sides with letters. Follow a billiard ball trajectory around the surface and record the "bounce sequence," or the sequence of labels hit by the ball as it moves. Is it possible for two different billiard tables to have all the same bounces?

Special Colloquium: Tuesday September 26, 4-5pm, JWB 335:
Speaker: David Higdon, Virginia Tech
Title: A small, biased sample of experiences involving statistical modeling and big data
Abstract: Statistical modeling is the art of combining mathematical/probabilistic models and data to infer about some real-life system. The structure, volume and diversity of modern data sources brings out a number of computational challenges in applying statistical modeling to such data. This talk will cover three different examples that grapple with big data and computational issues in statistical inference: computer model calibration for cosmological inference; response surface/regression modeling in big data settings; combining varieties of automatically collected data to better manage a supply chain of a large industrial corporation. A bit more technical detail will be given for the first example in cosmology where observations are combined with computational model runs carried out at different levels of resolution to infer about parameters in the standard model. The other two applications will be discussed from a broader perspective, motivating thoughts regarding commonalities and differences in these different strategies for big data analytics.

November 2:
Speaker: Sarang Joshi, University of Utah
Title: Riemannian Brownian Bridges and Metric Estimation on Landmark Manifolds
Abstract: We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric. The distribution possesses properties similar to the regular Euclidean normal distribution but its transition density is governed by a high-dimensional non-linear PDE with no closed-form solution. We show how the density can be numerically approximated by Monte Carlo sampling of conditioned Brownian bridges, and we use this to estimate parameters of the LDDMM kernel and thus the metric structure by maximum likelihood. (Joint with Stefan Sommer, Alexis Arnaudon, Line Kuhnel)

November 9:
Speaker: Benedek Valko, University of Wisconsin
Title: Random matrices, operators and carousels
Abstract: We show that some of the classical random matrix models and their beta-generalizations converge to random differential operators in a certain limit. The result connects the (i) Montgomery-Dyson conjecture about random matrices and the non-trivial zeros of the Riemann zeta function, (ii) the Hilbert-Polya conjecture, and (iii) de Brange’s approach of possibly proving the Riemann hypothesis. We combine probabilistic, functional analytic and geometric ideas, but special background knowledge of these topics is not required for the talk.

November 16 2:30-3:30pm: (Note special time)
Speaker: Claudia Polini, University of Notre Dame
Title: Syzygies and Singularities of Rational Curves
Abstract: We study rational curves in projective space, most notably rational plane curves, through the syzygy matrix of the forms parametrizing them. A rational plane curve C of degree d can be parametrized by three forms f_1,f_2,f_3 of degree d in the polynomial ring k[x,y], and the syzygy matrix F of these forms is easier to handle and often reveals more information than the implicit equation of C.
Our goals are to read information about the singularities of C solely from the matrix F, to set up a correspondence between the types of singularities on the one hand and the shapes of the syzygy matrices on the other hand, and to use this correspondence to stratify the space of rational plane curves of a given degree.
The constellation of singularities is also reflected in strictly numerical information about the Rees ring of the ideal (f_1, f_2, f_3), namely the first bigraded Betti numbers. The intermediary between singularity types and Rees algebras is once again the syzygy matrix F, or rather a matrix of linear forms derived from it.

November 30 2:30-3:30pm: (Note special time)
Speaker: Kathryn Bond Stockton, The University of Utah
Title: Beyond Diversity: Where We Are Is More Urgent and Conceptually Interesting Than You Think
Abstract: What, exactly, do you know about diversity efforts here at the U? Why are they more urgent than ever before? Prepare to hear these matters framed in ways that may surprise you, in ways that will reach to where and how you live and, of course, how you think. Needless to say, all departments need to talk in depth about these issues if they would be cutting-edge—and thrive.
Kathryn Bond Stockton, with her Ph.D. from Brown University and Master of Divinity from Yale University, is Distinguished Professor of English, Associate Vice President for Equity and Diversity, and inaugural Dean of the School for Cultural and Social Transformation at the University of Utah. In 2013 she was awarded the Rosenblatt Prize for Excellence, the highest honor granted by this university.

November 30 4:00-5:00pm: Math/CSME Colloquium
Speaker: Natasha Speer, The University of Maine
Title: Why did they think that? The use and development of mathematical knowledge for teaching at the undergraduate level
Abstract: When instructors help someone learn mathematics, they use the knowledge they have of mathematics. The work of teaching also involves a variety of other kinds of knowledge, including knowledge of how people may think, productively and unproductively, about particular ideas. During this talk, the audience will have opportunities to engage in some teaching-related tasks and to consider the knowledge doing so requires. I will share information about research done to define kinds of knowledge and to examine the roles it plays in teaching and learning, including my own on-going investigation of college instructors’ knowledge of student thinking about ideas in calculus.

December 7:
Speaker: Tim Austin, UCLA
Title: Measure concentration and the weak Pinsker property
Abstract: This talk is about the structure theory of measure-preserving systems: transformations of a finite measure space that preserve the measure. Many important examples arise from stationary processes in probability, and simplest among these are the i.i.d. processes. In ergodic theory, i.i.d. processes are called Bernoulli shifts. Some of the main results of ergodic theory concern an invariant of systems called their entropy, which turns out to be intimately related to the existence of `structure preserving' maps from a general system to Bernoulli shifts.
I will give an overview of this area and its history, ending with a recent advance in this direction. A measure-preserving system has the weak Pinsker property if it can be split, in a natural sense, into a direct product of a Bernoulli shift and a system of arbitrarily low entropy. The recent result is that all measure-preserving systems have this property.

Special Colloquium: Monday December 11, 4-5pm, JWB 335: (Note unusual day)
Speaker: Alex Wright, Stanford University
Title: Dynamics, geometry, and the moduli space of Riemann surfaces
Abstract: The moduli space of Riemann surfaces of fixed genus is one of the hubs of modern mathematics and physics. We will tell the story of how simple sounding problems about polygons, some of which arose as toy models in physics, became intertwined with problems about the geometry of moduli space, and how the study of these problems in Teichmuller dynamics lead to connections with homogeneous spaces, algebraic geometry, dynamics, and other areas. The talk will mention joint works with Alex Eskin, Simion Filip, Curtis McMullen, Maryam Mirzakhani, and Ronen Mukamel.

Spring 2018

Special Colloquium: Tuesday January 9, 4-5pm, JWB 335:
Speaker: Laura Schaposnik, University of Illinois at Chicago
Title: TBA
Abstract: TBA

Special Colloquium: Wednesday January 10:
Speaker: Jennifer Wilson, Stanford University
Title: Stability in the homology of configuration spaces
Abstract: This talk will illustrate some patterns in the homology of the configuration space F_k(M), the space of ordered k-tuples of distinct points in a manifold M. For a fixed manifold M, as k increases, we might expect the topology of these configuration spaces to become increasingly complicated. Church and others showed, however, that when M is connected and open, there is a representation-theoretic sense in which the homology groups of these spaces stabilize. In this talk I will explain these stability patterns, and describe higher-order stability phenomena -- relationships between unstable homology classes in different degrees -- established in recent work joint with Jeremy Miller. This project was inspired by work-in-progress of Galatius--Kupers--Randal-Williams.

Special Colloquium: Tuesday January 16, 4-5pm, JWB 335:
Speaker: Kevin Moon, Yale University
Title: TBA
Abstract: TBA

Special Colloquium: Thursday January 18, 4-5pm, JWB 335:
Speaker: Harish Bhat, UC Merced
Title: TBA
Abstract: TBA

Special Colloquium: Friday January 26, 3-4pm, JWB 335:
Speaker: Steven Sam, University of Wisconsin, Madison
Title: TBA
Abstract: TBA

Special Colloquium: Thursday February 1, 4-5pm, JWB 335:
Speaker: James Murphy, Johns Hopkins University
Title: TBA
Abstract: TBA

Tuesday March 6: (Note unusual date.)
Speaker: Wieslawa Niziol, CNRS/ENS de Lyon
Title: TBA
Abstract: TBA

March 8:Distinguished Lecture Series
Speaker: Yuri Tschinkel, New York University
Title: TBA
Abstract: TBA

March 15:
Speaker: José Gutiérrez, The University of Utah, College of Education
Title: TBA
Abstract: TBA

April 12:
Speaker: David Ayala, Montana State University
Title: TBA
Abstract: TBA

April 24 (Tuesday):
Speaker: Donna Testerman, EPFL
Title: TBA
Abstract: TBA