# MSCS Seminar Calendar

Monday August 31, 2015

**Model Theory Seminar**

First-order theories of II$_1$ factors-Part II

Isaac Goldbring (UIC)

2:00 PM in SEO 427

I will speak on a recent preprint (http://arxiv.org/pdf/1507.06340.pdf) proving that there are continuum many theories of II$_1$ factors. I will introduce all necessary background from the theory of von Neumann algebras.

**Graduate Student Colloquium**

An Introduction to the Theory of Cryptography

Adam Lelkes (UIC)

4:00 PM in SEO 636

This talk will be a brief introduction to the beautiful theoretical results in cryptography. Time permitting, we will answer questions such as:
1. Can you have perfect encryption? (Spoiler: yes, but it is impractical.)
2. Is there a notion of security that is practical but still hard enough to break? If so, can we achieve it?
3. Can we algorithmically generate pseudo-random bits? How random is random enough?
4. Is it possible to convince someone you proved the Riemann hypothesis without revealing any information at all about the proof itself?
5. You are talking to your friend on the phone and you want to decide an important question by flipping a coin. How can you make sure that your friend didn't lie about the result of the coin toss?

Tuesday September 1, 2015

**Logic Seminar**

Hindman’s theorem and idempotent types

Isaac Goldbring (UIC)

4:00 PM in SEO 427

For a set A of natural numbers, let FS(A) denote the set of sums of finitely many distinct elements of A. A set B of natural numbers is said to be an IP set if B contains FS(A) for some infinite set A. A central result in combinatorial number theory is Hindman's theorem, which states that if one finitely colors an IP set, then at least one of the colors is an IP set. The slickest proof of this result uses idempotent ultrafilters. Di Nasso suggested a model-theoretic generalization of idempotent ultrafilters, aptly named idempotent types, and asked in what completions of PA idempotent types exist. In this talk, I will show that Hindman's theorem is actually equivalent to the existence of idempotent types in all countable complete extensions of PA. This has potential philosophical consequences that I will also discuss. This is joint work with Uri Andrews.

Wednesday September 2, 2015

**Homotopy Theory Seminar**

Computations in algebraic K-theory

Benjamin Antieau (UIC)

2:00 PM in SEO 1227

I will survey some of the state of the art approaches to computing the algebraic K-theory of rings and schemes. This will include both rational perspectives and characteristic p methods such as the use of the Steenrod algebra, and it will give a kind of road map for where the seminar will go this semester.

**Graduate Algebraic Geometry Seminar**

Pathologies on surfaces in characteristic $p$, or how I found someone's paper is wrong

Xudong Zheng (UIC)

3:00 PM in SEO 712

In this talk, I will present some constructions of algebraic surfaces in characteristic $p$ which violate the Kodaira vanishing theorem. These surfaces also provide counterexamples to Fujita's positivity theorem for fibered surfaces. Further pathologies on these examples include the existence of non-closed global differential 1-forms and global vector fields, which are both known to be impossible in characteristic zero. I will survey the comparison of characteristic zero with characteristic $p$, sketch the construction, and mention how I encountered these results by noticing errors in a recent published paper.

**Graduate Geometry, Topology and Dynamics Seminar**

van Kampen's Theorem and Group actions on Trees

Edgar A. Bering IV (UIC)

3:00 PM in SEO 612

Starting with van Kampen's theorem we trace how a group splitting gives rise to an action on a tree. We will survey (but probably not prove)
converses and related structure theorems for groups one can obtain when the group acts on a tree. This talk will be accessible to anyone with a familiarity with van Kampen's theorem.

**Graduate Theoretical Computer Science Seminar**

Social choice theory and Fourier analysis: a simple proof of Arrow's Impossibility Theorem

Ben Fish (UIC)

3:00 PM in SEO 427

This talk will give an introduction to social choice theory, a theoretical framework for studying how to aggregate individual preferences into a social welfare function, concentrating on Arrow's Impossibility Theorem. This talk will present a proof of this theorem (due to Kalai, 2002) using the Fourier analysis of Boolean functions, which is both a surprising and elegant application of Fourier analysis.

**Algebraic Geometry Seminar**

Stability Conditions on Threefolds - Some Wall-Crossings

Benjamin Schmidt (Ohio State University)

4:00 PM in SEO 427

The theory of Bridgeland stability conditions has lead to deep results about the geometry of moduli spaces of sheaves on surfaces. One of the main obstacles to do the same on threefolds is the construction of stability conditions. Recent progress on this question in special cases raises the question whether the corresponding moduli spaces can be studied. I will present an approach that uses computations similar to those on surfaces. In the case of projective space, I will show examples of concrete wall-crossing behavior for some Hilbert schemes of curves.

Thursday September 3, 2015

**Quantum Topology / Hopf Algebra Seminar**

Rotational Virtual Knots and Quantum Invariants of Knots

Louis H Kauffman (UIC)

3:00 PM in SEO 612

We define rotational virtual knots and show how the KRH formulation of quantum invariants of knots and links fits precisely this diagrammatic category.
Thus rotational virtuals are the most natural test category for quantum invariants.

Tuesday September 8, 2015

**Logic Seminar**

A super-Dowker filter

James Cummings (CMU)

4:00 PM in SEO 427

A super-Dowker filter is a filter F on a set X such that
1) For every sequence of F-large sets there are x,y distinct with x in A_y and y in A_x
2) For every partition of X into two parts there exist a sequence as in 1) and a cell of the partition such that all pairs as in 1) lie in this cell
Building on work of Balogh and Gruenhage we show the consistency of the existence of a super-Dowker filter.

Wednesday September 9, 2015

**Graduate Geometry, Topology and Dynamics Seminar**

New Density Bounds and Optimal Ball Packings for Hyperbolic Space

Robert Kozma (UIC)

3:00 PM in SEO 612

We consider ball packings of hyperbolic space, motivating the discussion with recent developments in three dimensions.
We then show that it is possible to exceed the conjectured $4$-dimensional packing density upper bound due to L. Fejes-T\'oth (Regular Figures, 1964). We give several examples of horoball
packing configurations that yield higher densities of $\approx 0.71$ where horoballs are centered at the ideal vertices of certain Coxeter simplex tilings.

**Algebraic Geometry Seminar**

Calabi-Yau threefolds fibred by lattice polarized K3 surfaces

Alan Thompson (University of Waterloo)

4:00 PM in SEO 427

I will describe recent joint work with C. Doran, A. Harder and A. Novoseltsev, in which we study the moduli spaces of certain Calabi-Yau threefolds with small Hodge number $h^{2,1}$. Many such Calabi-Yau threefolds admit fibrations by K3 surfaces that are polarized by lattices of high rank. In the case where the polarizing lattice has rank 19, the theory of such fibrations closely parallels the theory of elliptic surfaces: in particular, the coarse moduli space of the K3 surface fibres is a modular curve, and there are analogues of the functional and homological invariants which determine much of the geometry of the threefold total space. Using this structure, it is possible to explicitly map out the moduli spaces of Calabi-Yau threefolds fibred by such K3 surfaces. There is also a beautiful interpretation of mirror symmetry for these Calabi-Yau threefolds, related to (weak) Landau-Ginzburg models of Fano threefolds, which I will describe if time allows.

Monday September 14, 2015

**Analysis and Applied Mathematics Seminar**

Semiclassical approximations to quantum mechanical expectation values

Wolfgang Gaim (University of Tübingen)

4:00 PM in SEO 636

In his 1932 paper, Eugene Wigner introduced the now famous Wigner function in order to compute quantum corrections to classical equilibrium distributions. We show how to extend this program and compute semiclassical approximations to time evolved quantum observables as well as quantum mechanical equilibrium distributions for slow, semiclassical degrees of freedom coupled to fast, quantum mechanical degrees of freedom. The main examples are molecules and electrons in crystalline solids. The semiclassical formulas contain, in addition to quantum corrections similar to those of Wigner, also modifications of the classical Hamiltonian system used in the approximation: The classical energy and the Liouville measure on classical phase space turn out to have non-trivial-expansions in the semiclassical parameter. This talk is based on joint work with Stefan Teufel.

Tuesday September 15, 2015

Wednesday September 16, 2015

**Geometry, Topology and Dynamics Seminar**

Knottedness is in NP, modulo GRH

Greg Kuperberg (UC Davis)

3:00 PM in SEO 636

In this talk I will discuss my result that confirming that a knot diagram is a non-trivial knot is in the complexity class NP, assuming the Generalized Riemann Hypothesis. Time permitting, I will also discuss related results, in particular the earlier result of Hass, Lagarias, and Pippenger that unknottedness is in NP. Everything will be on the theme of qualitative complexity theory in geometric topology, in other words, what you can compute in polynomial time with help.

Thursday September 17, 2015

**Quantum Topology / Hopf Algebra Seminar**

How hard is it to approximate the Jones polynomial?

Greg Kuperberg (UC Davis)

3:00 PM in SEO 612

The short answer is that it's #P-hard. The longer answer
is that it was an algorithm was constructed in the quantum computation
community to approximate the Jones polynomial at a principal root of
unity, except with a diagram-dependent normalization factor. I will
present my result that if you strip away this normalization factor to
ask for any fair approximation, then approximating the Jones
polynomial is as hard as any combinatorial counting problem and almost
certainly out of reach for classical or even quantum computers. It
is conjectured that the Jones polynomial distinguishes the unknot, but
we can envision that we can know whether a complicated knot diagram is
an unknot long before we know much about its Jones polynomial.

Monday September 21, 2015

**Analysis and Applied Mathematics Seminar**

Perturbation theory for discrete eigenvalues: Kato-Rellich theory and asymptotic expansions

George Nenciu (Institute of Mathematics of the Romanian Academy)

4:00 PM in SEO 636

Basic facts of Kato-Rellich regular perturbation for discrete eigenvalues are
briefly reviewed. For singular perturbations (e.g. anharmonic oscillator,
Stark effect) asymptotic expansions for the perturbed projections leading to
(almost) invariant subspaces are provided.
This is a two hour introductory talk intended mainly for graduate students.

Wednesday September 23, 2015

Friday September 25, 2015

Monday September 28, 2015

**Combinatorics Seminar**

The critical exponent of a graph

Apoorva Khare (Stanford University)

3:00 PM in SEO 427

We classify the powers that preserve positive semidefiniteness, when applied entrywise to matrices with rank and sparsity constraints. This is part of
a broad program to study entrywise functions preserving positivity on distinguished submanifolds of the cone. In our first main result, we completely
classify the powers preserving Loewner properties on positive semidefinite matrices with fixed dimension and rank. This includes the case where the
matrices have negative entries.
Our second main result characterizes powers preserving positivity on matrices with zeros according to a chordal graph. We show how preserving positivity
relates to the geometry of the graph, thus providing interesting connections between combinatorics and analysis. The work has applications in
regularizing covariance/correlation matrices, where entrywise powers are used to separate signal from noise, while minimally modifying the entries of
the original matrix. (Based on joint work with D. Guillot and B. Rajaratnam, Stanford.)

**Analysis and Applied Mathematics Seminar**

Perturbation theory for embedded eigenvalues: Rayleigh-Schrödinger expansion, spectral concentration and metastable states.

George Nenciu (Institute of Mathematics of the Romanian Academy)

4:00 PM in SEO 636

Perturbation theory for embedded eigenvalues and exponential decay for resulting metastable states are considered.
The relations between the formal Rayleigh-Schrödinger expansion, spectral concentration and decay law for metastable states are discussed in the smooth setting.
The main result is that if the FGR constant vanishes then the first order correction in the Rayleigh-Schrödinger expansion
is well defined and the exponential decay law for the corresponding metastable state has both the decay rate and error term of order $\epsilon^4$
where $\epsilon$ is the perturbation strength.

Wednesday September 30, 2015

**Algebraic Geometry Seminar**

Tropical Independence and the Maximal Rank Conjecture for Quadrics

David Jensen (University of Kentucky)

4:00 PM in SEO 427

The maximal rank conjecture, which has roots in the work of Noether and Severi in the late 19th and early 20th centuries, predicts the Hilbert function of the general embedding of a general curve. In recent joint work with Sam Payne, we show that this conjecture holds for the Hilbert function evaluated at $m=2$, meaning that such a curve is contained in the expected number of independent quadrics. From this we deduce that the general curve of genus $g$ and degree $d$ in projective space of dimension r is projectively normal if and only if $(r+2)(r+1)/2$ is at least $2d-g+1$. Our proof uses techniques from tropical and nonarchimedean geometry.

Thursday October 1, 2015

**Quantum Topology / Hopf Algebra Seminar**

Geometry of some unitary Riemann surface braid group representations and Laughlin-type wave functions.

Mauro Spera (Dipartimento di Matematica e Fisica "Niccolo' Tartaglia" Universita' Cattolica del Sacro Cuore, Bres)

3:00 PM in SEO 612

In this talk a construction of the simplest unitary Riemann surface braid group representations is outlined via stable holomorphic vector bundles over complex tori and the prime form on Riemann surfaces. Generalised Laughlin wave functions are then introduced. The genus one case is discussed in more detail also with the help of noncommutative geometric and of Fourier-Mukai-Nahm techniques, in view of elucidating the emergence of an intriguing Riemann surface braid group duality. The talk is based on the paper "On the geometry of some unitary Riemann surface braid group representations and Laughlin-type wave functions" J.Geom.Phys. 94 (2015),120-140.

Friday October 2, 2015

**Departmental Colloquium**

Mappings of complex and real analytic spaces

Dale Cutkosky (University of Missouri)

3:00 PM in SEO 636

We discuss some good properties of analytic mappings, including flatness, regularity and being locally monomial.
All of these properties can be obtained locally after performing suitable sequences of local blow ups.
Key notions are that of a star and the stellar vault, which were introduced by Hironaka.

Monday October 5, 2015

Wednesday October 7, 2015

**Statistics Seminar**

Design of Dose-response Clinical Trials

Naitee Ting (Boehringer-Ingelheim Pharmaceuticals Inc.)

4:00 PM in SEO 636

In the process of drug discovery and drug development, understanding the dose-response relationship is one of the most challenging tasks. It is also critical to identify the right range of doses in early stages of clinical development so that Phase III trials can be designed to confirm these doses. Usually at the beginning of Phase II, there is not a lot of available information to help guiding the study design. At this stage, Phase II clinical studies are needed to establish proof of concept (PoC), to identify a set of potentially effective and safe doses, and to estimate dose-response relationships.
Challenges in designing these studies include: selection of the dose frequency and the dose range, choice of clinical endpoints or biomarkers, and use of control(s), among others. Consequences of bad Phase II study designs may lead to the delay of the entire clinical development program or the waste of R&D investment. Misleading results obtained from poor designs could cause a Phase III program to confirm a wrong set of doses, or to stop developing a potentially useful drug. Therefore, it is critical to consider an entire drug development plan, to make best use of all the available information, and to include all relevant experts in designing Phase II dose response clinical trials. This presentation discusses some of these considerations.

Monday October 12, 2015

Wednesday October 14, 2015

Monday October 19, 2015

**Analysis and Applied Mathematics Seminar**

Semi-Analytical Time Differencing Methods for Stiff Problems

Chang-Yeol Jung (Ulsan National Institute of Science and Technology)

4:00 PM in SEO 636

A semi-analytical method is developed based on conventional integrating factor (IF) and exponential time differencing (ETD) schemes for stiff problems.
The latter means that there exists a thin layer with a large variation in their solutions. The occurrence of this stiff layer is due to the multiplication of a very small parameter $\epsilon$
with the transient term of the equation. Via singular perturbation analysis, an analytic approximation of the stiff layer, which is called a corrector, is sought for and embedded into the IF and ETD methods. These new schemes are then used to approximate the non-stiff part of the solution. Since the stiff part is resolved analytically by the corrector, the new method outperforms the conventional ones in terms of accuracy. In this paper, we apply our new method for both problems of ordinary differential equations and some partial differential equations.

Wednesday October 21, 2015

Friday October 23, 2015

Monday October 26, 2015

Wednesday October 28, 2015

Monday November 2, 2015

**Departmental Colloquium**

Adjacency and coherency preservers

Peter Semrl (University of Ljubljana, Slovenia)

3:00 PM in SEO 636

Two matrices are said to be adjacent if their difference is of
rank one. Fundamental theorems of geometry of matrices proved by L.-K.
Hua describe the general form of bijective maps on various spaces of
matrices preserving adjacency in both directions. We will present
several recent improvements of these results and some applications in
mathematical physics.

Wednesday November 4, 2015

Friday November 6, 2015

Monday November 9, 2015

Thursday November 12, 2015

Monday November 16, 2015

**Geometry, Topology and Dynamics Seminar**

A construction of limiting solutions of Hitchin's equations

Laura Fredrickson (University of Texas at Austin)

3:00 PM in SEO 636

I'll describe a construction of solutions of Hitchin's equations on a compact Riemann surface near the "ends" of the SL(n,C)-Hitchin moduli space. This construction generalizes Mazzeo-Swoboda-Weiss-Witt's construction of SL(2,C) solutions of Hitchin's equations where the Higgs field is "simple." In the generalized construction, moduli spaces of irregular connections arise. This is ongoing work.

Tuesday November 17, 2015

Wednesday December 2, 2015

Monday February 22, 2016

Friday February 26, 2016