# MSCS Seminar Calendar

Monday May 2, 2016

**Computer Science Seminar**

Learning Communities in the Presence of Errors

Aravindan Vijayaraghavan (Northwestern)

3:00 PM in SEO 612

The Stochastic Block Model or the Planted Partition Model is the most widely used probabilistic model for community detection and clustering graphs in various fields, including machine learning, statistics, and social sciences. Many existing algorithms successfully learn the communities or clusters when the data is drawn exactly according to the model, but they do not work well in the presence of errors. In this talk, I will address the following question:
Can we design robust polynomial time algorithms for learning probabilistic models for community detection that work in the presence of adversarial modeling errors?
I will present robust algorithms for (partially) recovering communities or clusters in graphs drawn from the Stochastic Block Model, in the presence of modeling errors or noise. These algorithms allow two types of adversarial errors: edge outlier errors (where an adversary can corrupt an arbitrary \epsilon fraction of the edges), and any amount of Feige-Kilian or monotone errors. Mossel, Neeman and Sly (STOC 2015) posed an open question about whether an almost exact recovery is possible when the adversary is allowed to add o(n) edges. Our work answers this question affirmatively even in the case of k>2 communities.
Finally, I will describe how our algorithms recover the clusters, even when the modeling error is captured using Kullback-Leibler (KL) divergence: these algorithms work when the instances come from any distribution of graphs that is \epsilon.m close to the Stochastic Block Model in the KL divergence (this result also handles adversarial errors).
This is based on joint work with Konstantin Makarchev and Yury Makarychev.

Wednesday May 4, 2016

**Number Theory Seminar**

A heuristic for boundedness of elliptic curves

Jennifer Park (University of Michigan)

1:00 PM in SEO 1227

I will discuss a heuristic that predicts that the ranks of all but finitely many elliptic curves defined over Q are
bounded above by 21. This is joint work with Bjorn Poonen, John Voight, and Melanie Matchett Wood.

Friday May 6, 2016

**Number Theory Seminar**

A p-adic strengthening of the Manin-Mumford conjecture

Vlad Serban (Northwestern)

11:00 AM in SEO 427

Let $G$ be an abelian variety or a product of multiplicative groups
$\mathbb{G}_m^n$ and let $C$ be an embedded curve. The Manin-Mumford
conjecture (a theorem by work of Lang, Raynaud et al.) states that only
finitely many torsion points of $G$ can lie on $C$ unless $C$ is in
fact
a subgroup of $G$. I will show how these purely algebraic statements
extend to suitable analytic functions on open $p$-adic unit poly-disks.
These disks occur naturally as weight spaces parametrizing families of
$p$-adic automorphic forms for $GL(2)$ over a number field $F$. When
$F=\mathbb{Q}$, the "Hida families" in question play a crucial role in
the study of modular forms. When $F$ is imaginary quadratic, I will
explain how our results imply that Bianchi modular forms are sparse in
these $p$-adic families.

Monday May 9, 2016

**Thesis Defense**

Moduli Spaces of Sheaves on $\mathbb{P}^1 \times \mathbb{P}^1$

Tim Ryan (UIC)

11:00 AM in SEO 636

In this talk, after reviewing the basic properties of moduli spaces of sheaves on $\mathbb{P}^1 \times \mathbb{P}^1$, I will show that they are $\mathbb{Q}$-factorial Mori Dream Spaces and explain a method for computing their effective cones. My method is based on the generalized Beilinson spectral sequence, Bridgeland stability, and moduli spaces of Kronecker modules.

Monday August 29, 2016

**Geometry, Topology and Dynamics Seminar**

Random Grids in G-spaces

Jayadev S. Athreya (University of Washington)

3:00 PM in SEO 636

We show how to define a general notion of a random grid, how it generalizes the notion of random Euclidean lattices and random affine lattices, and describe how it gives a natural notion of a random hyperbolic lattice. This is joint work with Gregory Margulis and Yair Minsky.

We will be going for a seminar dinner. Email schapos@uic.edu if you'd like to join.

Wednesday September 7, 2016

Monday September 26, 2016