# MSCS Seminar Calendar

Tuesday January 17, 2017

**Quantum Topology / Hopf Algebra Seminar**

Knots and Graphs

Louis Kauffman (UIC)

2:00 PM in SEO 612

This talk will be an introduction to the reformulation of knot theory in terms of special moves on signed
planar graphs, derived from the checkerboard coloring of a knot diagram. The talk is entirely elementary
and self-contained and is of interest to students of topology and/or graph theory

**Special Colloquium**

Parsimonious Modeling of the Inverse Regression

Aaron Molstad (University of Minnesota)

3:00 PM in SEO 636

In the first part of the talk, we propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly estimate the regression coefficient matrix through shrinkage estimation of the parameters of the inverse regression, or the conditional distribution of the predictors given the responses. We establish a convergence rate bound for estimators in our class. These estimators do not require the popular assumption that the forward regression coefficient matrix is sparse or has small Frobenius norm.
In this second part of the talk, we propose a penalized likelihood method to fit the linear discriminant analysis model when the predictor is matrix valued. We assume the precision matrix has a Kronecker product decomposition. Our penalties encourage pairs of response category mean matrix estimators to have equal entries and also encourage zeros in the precision matrix estimator. To compute our estimators, we use a blockwise coordinate descent algorithm. To update the optimization variables corresponding to response category mean matrices, we use an alternating minimization algorithm that takes advantage of the Kronecker structure of the precision matrix.

**Logic Seminar**

Definable Skolem functions for weakly o-minimal structures

Chris Shaw (Columbia College)

4:00 PM in SEO 427

In this talk we present an overview of progress on the question of which weakly o-minimal structures have definable Skolem functions. Given an o-minimal structure ${\mathcal M}$ expanding a group and a convex predicate $U$ interpreting a nonvaluational convex set, the structure $({\mathcal M}, U)$ fails to have definable Skolem functions, even after naming constants. More generally, any structure which is elementarily equivalent to a reduct of a model formed in this fashion will also fail to have definable Skolem functions. As a partial converse, when $({\mathcal M},U)$ is valuational, modulo adding constants, the expanded structure in fact does have definable Skolem functions. Time permitting, we will give some insight into algorithms that may be used to calculate these functions where they are present.

We will meet for lunch at noon on the first floor of SEO.

Wednesday January 18, 2017

**Model Theory Seminar**

Ax-Lindemann-Weierstrass for abelian varieties I

Dave Marker (UIC)

10:00 AM in SEO 427

A key point in Pila's diophantine work are results characterizing when algebraic varieties in the uniformization of an abelian variety
project into algebraic varieties in the image. In these seminars, we will go through a new, elementary proof of this result due to Peterzil and Starchenko.

**Graduate Algebraic Geometry Seminar**

Moduli of Surfaces: Difficulties & Inroads, or: Things Fall Apart

Tabes Bridges (UIC)

3:00 PM in SEO 712

I will briefly review some history and state some relevant definitions, in particular the notion of a stable variety due to Kollár and Shepherd-Barron. I will then illustrate by example the greater subtleties that arise in studying families of surfaces. Finally, I will describe a few special cases in which progress has been made.

**Special Colloquium**

Promoting Similarity of Sparsity Structures in Integrative Analysis

Yuan Huang (Yale University)

3:00 PM in SEO 636

For data with high-dimensional covariates but small sample sizes, the analysis of a single dataset often suffers from a lack of power and poor reproducibility. The integrative analysis of multiple independent datasets provides an effective way of pooling information and outperforms single-dataset and several alternative multi-datasets methods. In this study, we consider penalized variable selection and estimation in integrative analysis. Advancing from the existing studies, we introduce a novel penalty to explicitly encourage the similarity of sparsity structures. This study is motivated by the practical consideration that under many scenarios, multiple datasets are expected to share common important covariates. Theoretically the proposed method has established selection and estimation consistency properties under the high dimensional settings. Numerically the proposed method has identification and estimation performance better than or comparable to the alternatives under a wide spectrum of simulation scenarios. In the analysis of three lung cancer datasets with gene expression measurements, the proposed method identifies genes with sound biological implications and satisfactory prediction performance.

**Graduate Geometry, Topology and Dynamics Seminar**

Introduction to Hyperbolic Space

Ellie Dannenberg (UIC)

3:00 PM in SEO 612

This semester, we're reading Casson and Bleiler's Automorphisms of Surfaces after Nielsen and Thurston.
I'll be discussing section 1, which covers background material about hyperbolic space.

Thursday January 19, 2017

**Quantum Topology / Hopf Algebra Seminar**

Towards toposes and forcing: dependent types, toposes and presheaves

Jim Otto (UIC)

2:00 PM in SEO 612

We are working towards a double negation sheaves understanding of Cohen forcing,
roughly as in Johnstone's Dover book, but with P-names. We describe categories and toposes using
1st order dependent types. And we show that,
using the Yoneda lemma, categories of presheaves are toposes.

Friday January 20, 2017

**Special Colloquium**

Informative sampling of large database

Prof. Wei Zheng (Indiana University–Purdue University Indianapolis)

3:00 PM in SEO 636

For many tasks of data analysis, a large database of explanatory variables is readily available,
however, the responses are missing and expensive to obtain. A natural remedy is to judiciously select a
sample of the data, for which the responses are to be measured. In this paper, we adopt the classical
criteria in design of experiments to quantify the information of a given sample. Then, we provide a
theoretical justification for approximating the optimal sample problem by a continuous problem, for which
fast algorithms can be further developed with the guarantee of global convergence. Our approach exhibits
the following features: (i) The statistical efficiency of any candidate sample can be evaluated without
knowing the exact optimal sample; (ii) It can be applied to a very wide class of statistical models; (iii)
It can be integrated with a broad class of information criteria; (iv) It is scalable for big data.

Monday January 23, 2017

**Commutative Algebra Seminar**

Functorial Test modules

Axel Stabler (University of Michigan)

1:00 PM in SEO 427

In my talk I will report on joint work with Manuel Blickle. I will explain how one can generalize the definition of test ideals \tau to so-called Cartier modules in a functorial way. We obtain several transformation rules with respect to f^! and f_* for various classes of morphisms f: X \to Y, e.g. for f smooth one has an isomorphism f^! \tau = \tau f^!. Part of the reason for working in this generality is that one has an equivalence with constructible etale p-torsion sheaves up to nilpotence of Cartier modules and these results further support the idea that the test module construction relates to etale nearby cycles similarly to the complex situation where multiplier ideals relate to complex nearby cycles.

**Algebraic Geometry Seminar**

Stability on valuations of a singularity

Chenyang Xu (MIT / BICMR)

4:00 PM in SEO 427

In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which in particular reflects whether the Fano variety carries a canonical metric. In this talk, we will discuss a recent joint work with Chi Li (some part still in progress) in which we want to establish a local stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to degenerate the singularity to a K-semistable T-singularity (with a torus action) in the Sasakian-Einstein sense.

Tuesday January 24, 2017

**Logic Seminar**

Truncation in the Differential Field of Transseries

Santiago Camacho (UIUC)

4:00 PM in SEO 427

The theory of analyzable functions is based on the idea that certain classes of (germs of) functions equipped with a valuation can be understood by embedding them into fields of generalized series. One such clear example is the case of Analytic functions and Taylor expansions. We are interested in the cases in which this embedding can be obtained in a truncation closed way. That is embeddings in which all truncations of a series in the image of the embedding belong to the image as well. We will recall previously known results for certain classes of valued fields, and when can a truncation closed embedding be extended to specific ring extensions. We will then present results in the cases of differential ring and differential field extensions. We will conclude with an application in the field of Logarithmic-Exponential Transseries.

Monday January 30, 2017

**Geometry, Topology and Dynamics Seminar**

Kirwan surjectivity for quiver varieties

Tom Nevins (UIUC)

3:00 PM in SEO 636

Many interesting hyperkahler, or more generally holomorphic symplectic, manifolds are constructed via hyperkahler/holomorphic symplectic reduction. For such a manifold there is a “hyperkahler Kirwan map,” from the equivariant cohomology of the original manifold to the reduced space. It is a long-standing question when this map is surjective (in the Kahler rather than hyperkahler case, this has been known for decades thanks to work of Atiyah-Bott and Kirwan). I’ll describe a resolution of the question (joint work with K. McGerty) for Nakajima quiver varieties: their cohomology is generated by Chern classes of “tautological bundles.” If there is time, I will explain that this is a particular instance of a general story in noncommutative geometry. The talk will not assume prior familiarity with any of the notions above.

Wednesday February 1, 2017

**Algebraic K-Theory Seminar**

The transfer in algebraic K-theory and THH

Cary Malkiewich (UIUC)

1:00 PM in SEO 1227

Let R -> A be a map of rings or ring spectra, and suppose that A is perfect (finitely generated projective) as an R-module. Then in addition to the usual map on algebraic K-theory K(R) -> K(A), there is a wrong-way "transfer" map K(A) -> K(R). In particular, when E -> B is a map of spaces whose homotopy fiber F is finitely dominated, this gives a wrong-way map on Waldhausen's functor A(B) -> A(E). We will ask a few fundamental questions about this transfer, and present the beginning of a program to answer these questions using trace methods. Our main results concern the corresponding transfer on THH, which in the A-theory case is a stable map of free loop spaces LB_+ -> LE_+. If there is time, we will also describe how our techniques are related to the study of fixed points of dynamical systems.

Monday February 6, 2017

**Geometry, Topology and Dynamics Seminar**

Geometry and dynamics of free group automorphisms

Caglar Uyanik (UIUC)

3:00 PM in SEO 636

A common theme in geometric group theory is to obtain structural results about infinite groups by analyzing their action on metric spaces. In this talk, I will focus on two geometrically significant groups; mapping class groups and outer automorphism groups of free groups.We will describe a particular instance of how the dynamics and geometry of their actions on various spaces provide deeper information about the groups.

Friday February 10, 2017

Monday February 13, 2017

**Combinatorics Seminar**

On the Ramsey-Turan number with small independence number

Andrzej Dudek (Western Michigan)

2:00 PM in SEO 612

In this talk we consider the following question motivated by the classical Turan and Ramsey theorems. What is the maximum number of edges in a K_t-free graph G of order n with the s-independence number smaller than f(n) (where the s-independence number is the maximum number of vertices in a K_s-free induced subgraph of G)? This problem attracted a considerable amount of attention and has been mainly studied for f not too much smaller than n. In this talk we consider f(n) = n^d for d<1. In particular, we show that the maximum number of edges in a K_{s+1}-free graph of order n with the s-independence number at most n^d (for any 1/2 < d < 1) is roughly speaking n^{1+d}.

Monday February 20, 2017

Wednesday February 22, 2017

Monday February 27, 2017

**Computer Science Seminar**

Complete Derandomization of Identity Testing of Read-Once Formulas

Ilya Volkovich (University of Michigan)

2:00 PM in SEO 612

In this paper we study the identity testing problem of arithmetic read-once formulas (ROF) and some related models. A read-once formula is formula (a circuit whose underlying graph is a tree) in which the operations are {+, ×} and such that every input variable labels at most one leaf. We obtain the ﬁrst polynomial-time deterministic identity testing algorithm that operates in the black-box setting for read-once formulas, as well as some other related models. As an application, we obtain the ﬁrst polynomial-time deterministic reconstruction algorithm for such formulas. Our results are obtained by improving and extending the analysis of the algorithm of Shpilka-Volkovich 09’.
Joint work with Daniel Minahan.

Monday March 6, 2017

Tuesday March 7, 2017

Friday March 10, 2017

Tuesday March 14, 2017

Wednesday March 15, 2017

Monday March 27, 2017

Wednesday March 29, 2017

Friday March 31, 2017

Monday April 3, 2017

Monday April 10, 2017

Wednesday April 12, 2017

Monday April 17, 2017

Wednesday April 19, 2017

Friday April 21, 2017

Monday April 24, 2017

Wednesday April 26, 2017