# MSCS Seminar Calendar

Monday September 18, 2017

**Geometry, Topology and Dynamics Seminar**

A matrix model for random nilpotent groups

Tullia Dymarz (University of Wisconsin, Madison)

3:00 PM in SEO 636

In Gromov's density model, a random group is either trivial or hyperbolic and in particular never nilpotent. We use the fact that every torsion free nilpotent group can be realized as a subgroup of the group of all upper triangular matrices with integer entries to present a model for random nilpotent groups. Our random nilpotent groups are subgroups of this group of matrices generated by elements given by random walks on a fixed generating set. By varying the size of the matrices and the length of the subgroup generators we prove results on the 'step' (i.e. the length of the lower central series) of a random nilpotent group. This is joint work with K. Delp and A. Schaffer-Cohen.

**Analysis and Applied Mathematics Seminar**

Dynamics of singularities and wavebreaking in 2D hydrodynamics with free surface

Pavel Lushnikov (University of New Mexico)

4:00 PM in SEO 636

2D hydrodynamics of ideal fluid with free surface is considered. A
time-dependent conformal transformation is used which maps a free
fluid surface into the real line with fluid domain mapped into the
lower complex half-plane. The fluid dynamics is fully characterized
by the complex singularities in the upper complex half-plane of the
conformal map and the complex velocity. The initially flat surface
with the pole in the complex velocity turns over arbitrary small
time into the branch cut connecting two square root branch points.
Without gravity one of these branch points approaches the fluid
surface with the approximate exponential law corresponding to the
formation of the fluid jet. The addition of gravity results in
wavebreaking in the form of plunging of the jet into the water
surface. The use of the additional conformal transformation to
resolve the dynamics near branch points allows to analyze
wavebreaking in details. The formation of multiple Crapper capillary
solutions is observed during overturning of the wave contributing to
the turbulence of surface wave. Another possible way for the
wavebreaking is the slow increase of Stokes wave amplitude through
nonlinear interactions until the limiting Stokes wave forms with
subsequent wavebreaking. For non-limiting Stokes wave the only
singularity in the physical sheet of Riemann surface is the
square-root branch point located. The corresponding branch cut
defines the second sheet of the Riemann surface if one crosses the
branch cut. The infinite number of pairs of square root
singularities is found corresponding to infinite number of
non-physical sheets of Riemann surface. Each pair belongs to its own
non-physical sheet of Riemann surface. Increase of the steepness of
the Stokes wave means that all these singularities simultaneously
approach the real line from different sheets of Riemann surface and
merge together forming 2/3 power law singularity of the limiting
Stokes wave. It is conjectured that non-limiting Stokes wave at the
leading order consists of the infinite product of nested square root
singularities which form the infinite number of sheets of Riemann
surface. The conjecture is also supported by high precision
simulations, where a quad (32 digits) and a variable precision (up
to 200 digits) were used to reliably recover the structure of square
root branch cuts in multiple sheets of Riemann surface.

Tuesday September 19, 2017

**Quantum Topology / Hopf Algebra Seminar**

Quantum Link Invariants

Louis H Kauffman (UIC)

3:00 PM in SEO 612

Continuing. We have constructed a solution to the Yang-Baxter Equation that generalizes the solution corresponding
to the bracket polynomial, but supported by any ordered index set. We have used this to construct state sum
models for the Homflypt polynomial. We continue this discussion and its relationship with Hecke algebras.

Wednesday September 20, 2017

**Algebraic K-Theory Seminar**

Infinite loop spaces in algebraic geometry

Elden Elmanto (Northwestern)

10:30 AM in SEO 1227

A classical theorem in modern homotopy theory states that functors from finite pointed sets to spaces satisfying certain conditions model infinite loop spaces (Segal 1974). This theorem offers a recognition principle for infinite loop spaces. The analogous theorem for Morel-Voevodsky's motivic homotopy theory has been sought for since its inception. In joint work with Marc Hoyois, Adeel Khan, Vladimir Sosnilo and Maria Yakerson, we provide such a theorem. The category of finite pointed sets is replaced by a category where the objects are smooth schemes and the maps are spans whose "left legs" are finite syntomic maps equipped with a K-theoretic trivialization of its contangent complex. I will explain what this means and how it is not so different from finite pointed sets. Time permitting, I will also provide an explicit model for the motivic sphere spectrum as a torsor over a Hilbert scheme.

**Graduate Geometry, Topology and Dynamics Seminar**

Geometric categories

Janis Lazovskis (UIC)

3:00 PM in SEO 612

I will describe an analogy between the basic building blocks of topological spaces, simplicial complexes, and the basic building blocks of algebra, categories. The main goal will be to interpret algebraic constructions through topological intuition.

**Graduate Analysis Seminar**

An Introduction to the Monodromy Representation

Charles Alley (UIC)

4:00 PM in SEO 512

The Monodromy Representation is a representation of the fundamental group of a Riemann surface into GL(n,C). In this talk I will survey the classical perspective on Monodromy from the theory of ordinary differential equations in the complex domain. This will be the first of two talks; the second talk will be focused on generalized monodromy which incorporates data arising from Stokes phenomenon.

Thursday September 21, 2017

**Louise Hay Logic Seminar**

VC Dimension, VC Density, and the Sauer-Shelah Dichotomy - Part I

Roland Walker (UIC)

1:00 PM in SEO 427

Vapnik-Chervonenkis dimension and density are two measures of combinatorial complexity which arose from the study of probability theory. During this two-part talk, we will discuss these measures and their duals both in the classical and model-theoretic contexts, prove the famous Sauer-Shelah Lemma, discuss the relationship between VC dimension and NIP, and time permitting discuss some recent applications and open questions.

**Quantum Topology / Hopf Algebra Seminar**

What is a Rotweldid Knot?

Jonathan Schneider (UIC)

3:00 PM in SEO 612

This series of talks represents joint work with Eiji Ogasa and Lou Kauffman.
Shin Satoh provided a topological model for the diagrammatic theory of
Welded knots. Specifically, he described a map from knot diagrams to
toral surfaces which respects Welded-equivalence, so equivalent diagrams
are modeled by isotopic toral surfaces.
However, Satoh was unable to determine whether this model
was classifying for Welded knot theory— whether inequivalent
Welded knot diagrams might nonetheless be modeled by isotopic toral surfaces. The question of whether Satoh’s model is classifying remains open as of 2017.
Colin Rourke claimed to provide another model for Welded knot theory,
based on Satoh’s model but “strengthened”. In his proposal, Rourke
adorned Satoh’s toral surfaces with a fiber-structure. Under this construction, inequiv- alent knot diagrams never map to fiberwise-isotopic toral surfaces, so Rourke’s model— if it is a valid model at all— is a classifying model for the theory.
Unfortunately, Rourke’s construction is not invariant of Welded knot type
, thus it is not a valid model for Welded knot theory. This is Main Theorem 1 of the present paper. We prove the theorem by exhibiting two knot diagrams which are Welded-equivalent, but whose Rourke-models are not fiberwise-isotopic.
1. Rourke’s construction is thus useless as a model for Welded knot theory. However, the theory can be modified into a new diagrammatic theory, which we call Rotweldid knot theory, by omitting the single Welded Reidemeister move where Rourke’s invariance proof failed. The invariance of Rourke’s construction as a model for Rotweldid knot theory is our Main Theorem 2. The proof is the same as Rourke’s erroneous proof for Weldid, with the bad part excised.
Not only is Rourke’s construction a valid model for Rotweldid knot theory,
it also happens to be a classifying model. This is our Main Theorem 3.

**Logic Seminar**

Constructing Analyzable Types in Differentially Closed Fields with Logarithmic Derivatives

Ruizhang Jin (Waterloo)

4:00 PM in SEO 427

We generalize the well-known fact that the equation $\delta(\mathrm {log}\delta x)=0$ is analyzable in but not internal to the constants. We use the logarithmic derivative as a building block to construct analyzable types with a unique analysis of minimal length (up to interalgebraicity). We also look for criteria for a given definable set such that its pre-image under the logarithmic derivative is analyzable in but not internal to the constants.

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

Friday September 22, 2017

**Departmental Colloquium**

Vortex filament dynamics

Walter Craig (McMaster University)

3:00 PM in SEO 636

The evolution of vortex filaments in three dimensions is a question of mathematical hydrodynamics which involves the analysis of nonlinear partial differential equations. On the physical side it is relevant to questions of vortex evolution for the Euler equations as well as to the fine structure of vortex cores in a superfluid. On the mathematical side it is a setting of partial differential equations with a compelling analogy to Hamiltonian dynamical systems. In this lecture I will describe a model for the dynamics of near - parallel vortex filaments and their mutual interactions in a three dimensional fluid. The talk will describe a phase space analysis of solutions, including constructions of periodic and quasi-periodic orbits via a version of KAM theory in an infinite dimensional phase space, and a topological principle to count the multiplicity of solutions. This is ongoing joint work with L. Corsi (Georgia Institute of Technology), C. Garcia (UNAM) and C.-R. Yang (McMaster and Shantou University)

Tea 4:15 PM

Monday September 25, 2017

**Graduate Infinity Categories Seminar**

Infinity Categories: Examples and Applications

Gregory Taylor (UIC)

10:00 AM in SEO 1227

We explore the utility of infinity categories in various areas of mathematics. Topics (may) include (but are not limited to) TQFTs and the Cobordism Hypothesis, locally constant sheaves, and (Derived) Algebraic Geometry.

Tuesday September 26, 2017

**Logic Seminar**

Variations of the stick principle

William Chen (Ben-Gurion University)

4:00 PM in SEO 427

The stick principle is a weakening of Jensen's diamond that asserts that there is a family of infinite subsets of $omega_1$ so that any uncountable subset of $\omega_1$ has some member of the family as a subset. We will give a forcing construction to separate versions of the stick principle which put a bound on the order-type of the subsets in the family. Many open problems remain about the relationship between different variations of this principle, such as the existence of certain club-guessing sequences or Suslin trees, and we will describe some progress in this direction.

Wednesday September 27, 2017

**Algebraic K-Theory Seminar**

Chern characters of perfect modules over curved algebras

Michael Brown (UW-Madison)

10:30 AM in SEO 1227

This is a report on joint work with Mark Walker. Let k be a field of characteristic 0, and let A be a smooth, essentially finite type k-algebra. The classical Hochschild-Kostant-Rosenberg isomorphism identifies the periodic cyclic homology of A with its de Rham cohomology. Moreover, classical Chern-Weil theory provides an explicit formula for the Chern character of a projective A-module in terms of this identification. The goal of this project is to generalize this story to the setting of "curved algebras", i.e. graded k-algebras equipped with a specified degree 2 element. In this talk, I will recall a well-known generalization of the HKR theorem to the setting of curved algebras, and I will discuss a Chern-Weil-type formula for the Chern character of perfect modules over curved algebras satisfying an appropriate smoothness condition.

**Statistics Seminar**

Weighted limit theorems and applications

Yanghui Liu (Purdue University)

4:00 PM in SEO 636

The term “limit theorem” is associated with a multitude of statements having to do with the convergence of probability distributions of sums of increasing number of random variables. Given that a limit theorem result holds, “weighted limit theorem” considers the asymptotic behavior of the corresponding weighted sums. The weighted limit theorem problem has drawn a lot of attention in recent articles due to its key role in topics such as parameter estimations, Ito’s formula in law, time-discrete numerical schemes, and normal approximations, and various “unexpected” weighted limit theorems have been discovered since then. The purpose of this talk is to introduce a general framework and a transferring principle for this problem, and to provide improvement of the existing results in a few aspects.

Thursday September 28, 2017

**Louise Hay Logic Seminar**

VC Dimension, VC Density, and the Sauer-Shelah Dichotomy - Part II

Roland Walker (UIC)

1:00 PM in SEO 427

Vapnik-Chervonenkis dimension and density are two measures of combinatorial complexity which arose from the study of probability theory. During this two-part talk, we will discuss these measures and their duals both in the classical and model-theoretic contexts, prove the famous Sauer-Shelah Lemma, discuss the relationship between VC dimension and NIP, and time permitting discuss some recent applications and open questions.

Friday September 29, 2017

**Departmental Colloquium**

Kahler-Einstein metrics

Gabor Szekelyhidi (University of Notre Dame)

3:00 PM in SEO 636

Kahler-Einstein metrics are of fundamental importance in
Kahler geometry, with connections to algebraic geometry, geometric
analysis, string theory amongst other fields. Their study has received
a great deal of attention recently, culminating in the solution of the
Yau-Tian-Donaldson conjecture, characterizing which complex manifolds
admit Kahler-Einstein metrics. I will give an overview of the field,
including some recent developments.

Wednesday October 4, 2017

**Statistics Seminar**

Joint Estimation of Fractal Indices for Bivariate Gaussian Processes

Yimin Xiao (MSU)

4:00 PM in SEO 636

Multivariate (or vector-valued) stochastic processes are important in probability, statistics and various scientific areas as stochastic models. In recent years, there has been increasing interest in investigating their statistical inference and prediction.
In this talk, we study the problem for estimating jointly the fractal indices of a bivariate Gaussian process. These indices not only determine the smoothness of each component process, fractal behavior of the whole process, but also play important roles in characterizing the dependence structure among the components.
Under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators for bivariate fractal indices. Our main results show the effect of the cross dependence structure on the performance of the estimators.
This is a joint paper with Yuzhen Zhou.

Friday October 6, 2017

**Departmental Colloquium**

Images, PDEs and hierarchical construction of solutions with critical regularity

Eitan Tadmor (University of Maryland)

3:00 PM in SEO 636

Edges are noticeable features in images which can be extracted from noisy data using different variational
models. The analysis of such models leads to the question of representing general L^2-data as the
divergence of uniformly bounded vector fields.
We use a multi-scale approach to construct uniformly bounded solutions of div U=f for
general f’s in the critical regularity space L^2(T^2). The study of this equation and related
problems was motivated by recent results of Bourgain & Brezis. The intriguing critical aspect
here is that although the problems are linear, construction of their solution is not. These
constructions are special cases of a rather general framework for solving linear equations in
representations U=\sum_j u_j which we introduced earlier in the context of image processing,
yielding a multi-scale decomposition of "image" U.

Tuesday October 10, 2017

**Logic Seminar**

Borel Complexity and the Schroder-Bernstein Property

Douglas Ulrich (Maryland)

4:00 PM in SEO 427

Borel Complexity and the Schroder-Bernstein Property
I describe some new techniques for proving non-Borel reducibility results, and give some applications, including: suppose the collection of countable models of a sentence sigma of L_{omega_1 omega} satisfies the Schroder-Bernstein property, that is, if two countable models are bi-embeddable then they are isomorphic. Then, assuming a mild large cardinal, sigma is not Borel complete.

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

Friday October 13, 2017

Monday October 16, 2017

**Statistics Seminar**

Data Science 2.0

Dan Spillane (IBM)

4:00 PM in SEO 636

What's the purpose of Data Science anyway? In this discussion we'll explore how we need to turn data science upside-down to create the real value of this powerful trade. We need to push desired (business, social, economic...) outcomes to the forefront (the hypothesis) and leverage data, data platforms and AI to develop the questions we don't even know to ask and then help answer. We need to be data pioneers not just data engineers. Looking forward to a fruitful and living dialogue on Data Science 2.0.

Monday October 23, 2017

**Mathematics Computer Science Seminar**

Graph Pressing Sequences and Binary Linear Algebra

Joshua Cooper (University of South Carolina)

10:00 AM in SEO 612

One can construct a useful metric on genome sequences by computing minimal-length sortings of (signed) permutations by reversals. Hannenhalli and Pevzner famously showed that such sorting sequences are essentially equivalent to a certain sequences of operations -- ``vertex pressing'' -- on bicolored (aka loopy) graphs. We examine the matrix algebra over GF(2) that arises from the theory of such sequences, providing a collection of equivalent conditions for their existence and showing how linear algebra, poset theory, and group theory can be used to study them. We discuss enumeration, characterization, and recognition of uniquely pressable graphs (those with exactly one pressing sequence); a relation on pressing sequences that has a surprisingly diverse set of characterizations; and some open problems.

Please note the unusual time and room.

**Geometry, Topology and Dynamics Seminar**

Translation-like actions of nilpotent groups

Mark Pengitore (Purdue University)

3:00 PM in SEO 636

Whyte introduced translation-like actions of groups which serve as geometric generalization of subgroup containment. He then proved a geometric reformulation of the von Neumann conjecture by demonstrating a finitely generated group is nonamenable if and only if it admits a translation-like action by a non-abelian free group. This provides motivation for the study of what groups can translation-like on other groups. As a consequence of Gromov's polynomial growth theorem, only nilpotent groups can act translation-like on other nilpotent groups. In joint work with David Cohen, we demonstrate if two nilpotent groups have the same growth, but non-isomorphic Carnot completions, then they can't act translation-like on each other.

Wednesday October 25, 2017

**Algebraic Geometry Seminar**

Frobenius twists of ample vector bundles

Daniel Litt (Columbia University)

4:00 PM in SEO 427

In 1987, Deligne and Illusie famously gave an algebraic proof of the degeneration of the Hodge-to-de Rham spectral sequence and the Kodaira vanishing theorem. Their methods have been used since (by Arapura and others) to prove strong vanishing theorems. I'll discuss their methods, a conjecture that would strengthen them, and a proof of some important special cases of that conjecture. I'll also give some applications to toric varieties.

Friday October 27, 2017

Monday October 30, 2017

Wednesday November 1, 2017

Friday November 3, 2017

Monday November 6, 2017

**Algebraic Geometry Seminar**

The space of equations for a curve of prescribed gonality

Dhruv Ranganathan (MIT)

4:00 PM in SEO 427

The Brill-Noether varieties of a curve C parameterize embeddings of C of prescribed degree into a projective space of prescribed dimension, i.e. equations for the curve. When C is general, these varieties are well understood: they are smooth, irreducible, and have the "expected" dimension. As one ventures deeper into the moduli space, past the general curve, these varieties exhibit intricate, even pathological, behaviour: they can be highly singular and their dimensions are unknown. A first measure of the failure of a curve to be general is its gonality. Based on an analogous combinatorial problem on graphs, Pflueger conjectured a formula for the dimensions of the Brill-Noether varieties for general curves of a given gonality. I will present joint work with Dave Jensen, in which we prove Pflueger’s conjecture. The proof blends non-archimedean analytic techniques, ideas from logarithmic Gromov-Witten theory, and the geometry of scrolls.

Monday November 13, 2017

Wednesday November 15, 2017

**Algebraic Geometry Seminar**

Dominating varieties by liftable ones

Remy van Dobben de Bruyn (Columbia University)

4:00 PM in SEO 427

Given a smooth projective variety over an algebraically closed field of positive characteristic, can we always dominate it by another smooth projective variety that lifts to characteristic 0? We give a negative answer to this question.

Monday November 20, 2017

Wednesday November 22, 2017

Wednesday November 29, 2017

Monday December 4, 2017

Wednesday December 6, 2017

Friday February 16, 2018

Friday March 9, 2018

Friday March 23, 2018

Wednesday April 25, 2018