# Colloquium

The Colloquium is held on Mondays at 4pm in Deady 208.

### Fall Quarter, 2017

- September 25, No Colloquium
- October 2, No Colloquium
- October 9,
**Samuel Coskey** (Boise State University)

Borel complexity theory and classification problems
**Abstract**: Borel complexity theory is the study of the relative complexity of classification problems in mathematics. At the heart of this subject is invariant descriptive set theory, which is the study of equivalence relations on standard Borel spaces and their invariant mappings. The key notion is that of Borel reducibility, which identifies when one classification is just as hard as another. Though the Borel reducibility ordering is wild, there are a number of well-studied benchmarks against which to compare a given classification problem. In this talk we will introduce Borel complexity theory, present several concrete examples, and explore techniques and recent developments surrounding each.

- October 23,
**Kirsten Eisentraeger** (Pennsylvania State University)

Quantum algorithms and classical cryptography
**Abstract**: Computational problems that can be solved exponentially faster on a quantum computer than on a classical computer have mostly been number theoretic. It turns out that some of these problems, like factoring and the discrete log problem, are also required to be computationally difficult for certain cryptosystems to be secure. Hence RSA and Elliptic Curve Cryptography, that are based on the hardness of these problems, are not secure against quantum computers. In this talk I will discuss some recently proposed cryptosystems that have been suggested as alternatives to RSA and Elliptic Curve Cryptography. These fall into two categories, lattice-based systems and systems based on supersingular isogenies. We will discuss their security, both classically and against quantum computers.

- October 30,
**Mark Rudelson** (University of Michigan and MSRI)

Non-asymptotic approach in random matrix theory
- November 13,
**Dev Sinha** (UO)

Topological Data Analysis (&…)
**Abstract**: Topological data analysis aims to understand the shape of data sets, especially “large” ones, using tools from the relatively modern field of algebraic topology. We highlight two tools: the Reeb graph, which is organizes data graphically (as in, “with a graph,” but also as in “producing a picture”) with respect to a reference function, and persistent homology, which counts cycles in the data. We illustrate the effectiveness of these tools in three different settings: breast cancer, nanoporous materials, and neuroscience, drawing from papers from PNAS and Nature Comm. We will then also have some sociological discussion of the groups which have effectively done this work and musings about how such work – broadly defined to include the many areas of modern mathematics currently interfacing with science – could happen on our campus.

- November 27,
**Rafal LataĆa** (Warsaw/MSRI)

Upper and lower bounds for suprema of stochastic processes
**Abstract**: One of the fundamental questions of probability theory is the investigation of suprema of stochastic processes. Besides various practical motivations it is closely related to such important theoretical problems as boundedness and continuity of sample paths of stochastic processes, convergence of orthogonal series, random series and stochastic integrals, estimates of norms of random vectors and random matrices, limit theorems for random vectors and empirical processes, combinatorial matching theorems and many others.

The modern approach to this issue is based on the chaining methods. During the talk I will review several classical and more recent estimates for suprema of stochastic processes, discussing both lower and upper bounds. In particular I will present Dudley-Sudakov entropy-based bounds and Fernique-Talagrand generic chaining technique and will try to explore some of their applications and extensions.

- December 4,
**Kathryn Hess** (EPFL)

### Winter Quarter, 2018

- January 8,
**Jonathan Kujawa** (University of Oklahoma)
- January 15, No Colloquium – MLK Holiday
- February 5,
**Benson Farb** (University of Chicago)
- March 5,
**Henry Cohn** (Microsoft Research)

### Spring Quarter, 2018

**Previous years:** 2016 2015 2013 2012 2011 2010