# MSCS Seminar Calendar

Monday October 2, 2023

**MATH Club**

How to Apply to Graduate School Panel

Symbols of Inclusion (UIC)

1:00 PM in 636 SEO

Interested in applying for graduate school, or debating doing so alongside some other career options? Symbols of Inclusion will be hosting a panel with the Math Club on October 2nd to answer any questions you may have about the process. Sitting on the panel, we’ll have two first years, a third year, and a fourth year graduate student. Another fourth year will moderate. In this way, we hope to be able to accurately address questions about the process itself from students who just went through it, as well as any questions that require more experience in graduate school itself. Please come armed with questions!

**Algebraic Geometry Seminar**

Moduli of curves and K-stability

Junyan Zhao (UIC)

3:00 PM in 636 SEO

The K-moduli theory provides us with an approach to study moduli of curves. In this talk, I will introduce the K-moduli of certain log Fano pairs and how it relates to moduli of curves. We will see that the K-moduli spaces interpolate between different compactifications of moduli of curves. In particular, the K-moduli gives the last several Hassett-Keel models of moduli of curves of genus six.

**Combinatorics and Probability Seminar**

Polynomial computability of spectral radius of nonnegative tensors, uniform weighted hypergraphs, and related quantities

Shmuel Friedland (UIC)

3:00 PM in 612 SEO

The aim of this talk to show that several quantities as: the spectral radius
of weakly irreducible tensors, spectral radius of uniform weighted hypergraphs,
maximum of d-homogeneous polynomials with nonnegative coefficients in the
unit ball of the d-Holder norm, are polynomially computable. This computability result is proven for a larger class of minimum of certain convex functions
in R^n, which was considered by several authors. This is a joint work with
Stephane Gaubert, INRIA and Centre de Mathematiques Appliquees (CMAP),
Ecole polytechnique, IP Paris, France.

Note the unstandard time of 3PM rather than 2PM.

**Analysis and Applied Mathematics Seminar**

The HIGHWAVE project

Frederic Dias (University College Dublin)

4:00 PM in 636 SEO

The HIGHWAVE project (2019-2025) is primarily on wave breaking. The major
novelty during the first half of the project has been the experimental
campaign with a smart boulder. The data, obtained by altering the breaking
position of a wave impacting a vertical cliff, have demonstrated the
influence of wave-impact mode (aerated, breaking or sloshing) on the
displacement of clifftop boulders. This experimental campaign has shown
the range of wave focusing positions most conducive to boulder movement
and the range of displacement values we may expect in laboratory
experiments. The absence of multiple repeated tests and the inability to
fully quantify scaling effects mean that future work will firstly seek
to reliably extrapolate these laboratory boulder displacement
measurements to the real-world scale by quantifying pressure scaling
errors using large scale tests, carrying out a larger number of repeated
tests, and obtaining frictional similarity between prototype and
laboratory scales. Additionally, a comparison between the importance of
the wave-breaking position with the significant wave height and peak
wave period should be carried out.
At the beginning of the project we have been going back and forth between
what one would like to measure to better understand wave breaking and what
can be realistically measured in a hostile environment. The real
potential impact of our results will be the degree to which they are able
to describe real oceanic free surface profiles in a sea state where
breaking occurs. However, although we have been able to access a range
of data sets from wave buoys, ADCPs, radars, stereo vision, we have been
surprised to note the lack of reliability of measurements of breaking
wave events recorded in a given measurement time series or image as
measurements hit technical recording limits or generate artifacts in the
data. Indeed, we have come to realize that both the quality of the data
and the sophistication of data analysis of existing wave measurements
from sensors are based on decades-old technologies and methodologies and
are unsatisfactory for the detailed study of breaking waves.
Several theoretical results have been obtained as well: they range from
new limiting configurations for surface waves to new links between
superharmonic instability and wave breaking. Interesting results on wave
forecasting and on the effect of rain on waves will also be presented.
Acknowledgements: This work is funded by the European Research Council
(ERC) under the EU Horizon 2020 research and innovation programme (grant
agreement no. 833125-HIGHWAVE).

Tuesday October 3, 2023

**Logic Seminar**

On non-abelian dp-minimal groups

Atticus Stonestrom (University of Notre Dame)

4:00 PM in 636 SEO

Dp-minimality is a kind of abstract model-theoretic "one-dimensionality" condition, satisfied for example by superstable theories of U-rank 1 and o-minimal theories. In this talk we will introduce dp-minimality, and then discuss some results on dp-minimal groups: namely, every torsion-free dp-minimal group is abelian, every stable dp-minimal group is solvable-by-finite, and every distal dp-minimal group is nilpotent-by-finite.

Wednesday October 4, 2023

**Geometry/Topology Seminar**

The space of characters, its dynamics, and applications to arithmetic groups.

Itamar Vigdorovich (Weizmann)

3:00 PM in 636 SEO

To any group G is associated the space Ch(G) of all characters on G. After defining this space and discussing its interesting properties, I'll turn to discuss dynamics on such spaces. Our main result is that the action of any arithmetic group on the character space of its amenable/solvable radical is stiff, i.e, any probability measure which is stationary under random walks must be invariant. This generalizes a classical theorem of Furstenberg for dynamics on tori. Relying on works of Bader, Boutonnet, Houdayer, and Peterson, this stiffness result is used to deduce dichotomy statements (and 'charmenability') for higher rank arithmetic groups pertaining to their normal subgroups, dynamical systems, representation theory and more.
The talks is based on a joint work with Uri Bader.

At 1-2 we plan to go for lunch with the speaker. Please email furman@uic.edu if you would like to join.

**Dynamics Seminar**

A non-Euclidean “Linnik type” problem and statistics of orthogonal grids

Michael Bersudsky (The Ohio State University)

4:00 PM in 636 SEO

A classical work of Linnik shows that the directions of primitive integer vectors on a "large" sphere are "equidistributed". I will discuss a joint work with Uri Shapira in which we consider an analogue of Linnik's problem inside the special linear group. The motivation behind our study is an extension of a previous work of Uri Shapira, Menny Aka and Manfred Einsiedler concerning the statistics of orthogonal grids of primitive integral vectors.
I will present our results and a sketch of the main ideas in the proof – there’s a natural way to use the p-adics to generate integer points from a given integral point and to study those new points by looking on a certain periodic orbit in a homogeneous space.

Thursday October 5, 2023

**Louise Hay Logic Seminar**

Paradox, Cardinals, Gödel, and Cantor

Ryan Carpenter (UIC)

4:00 PM in 427 SEO

This sentence is false; or is it? In this talk, I will motivate a rather provincial viewpoint in the philosophy of mathematics (using Gödel's first incompleteness theorem) which embraces the existence of paradoxes, and I will detail one mathematician's attempt to take this viewpoint seriously. In doing so, we will discuss Cantor's theorem in both classical and paraconsistent settings, we'll investigate relevant set theory, and we'll do a bit of inconsistent reasoning along the way.

Friday October 6, 2023

**Departmental Colloquium**

Quantum correlations: from foundations to security against post-quantum eavesdropper

Pawel Horodecki (Gdańsk University of Technology)

3:00 PM in 636 SEO

Quantum mechanics allows quantum correlations – also called quantum entanglement – that are
stronger than all the correlations we know from our daily lives. Their enigma has already troubled
fathers of Quantum Mechanics. Einstein's ingenious skepticism about this theory gave rise to the
fundamental philosophical question - formalized mathematically by John Bell - about the objective
existence of properties of quantum particles before measurement.
We shall discuss the related Bell inequalities tests from the perspective of randomness and stress
that while quantum mechanical statistics look completely random, it may allow for a contribution of
determinism, if we look at them from the perspective of possible future physical theories. This rises
an interesting problem of certification of randomness and cryptographic security in hypothetical
situations where eavesdropper has a post-quantum power.
The two most natural post-quantum frameworks are the ones of no-signaling boxes and no-
signaling assamblages. We discuss quantum correlations from the perspectives of the two
frameworks. This includes on the one hand some no-go theorems and on the other hand some
positive results concerning randomness amplification and generation of secure bits.
[1] J. Barrett, L. Hardy, A. Kent, Phys. Rev. Lett. 95, 010503 (2005)
[2] R. Renner. R. Collbeck, Nat. Phys. 8, 450 (2012)
[3] F. G.S.L. Brandao, R. Ramanathan, A. Grudka, K. Horodecki, M. Horodecki, P. H., T. Szarek,
H. Wojewodka, Nat. Comm. 7, 11345 (2016)
[4] P. Horodecki and R. Ramanathan, Nat. Comm. 10,1701 (2019)
[5] R. Ramanathan, M. Banacki, R. Ravel Rodrigues, P. Horodecki, npj Quantum Information, 8,
119 (2022).
[6] M. Banacki, P. Mironowicz, R. Ramanathan, P. Horodecki, New J. Phys. 24, 083003 (2022)
[7] A. B. Sainz, N. Brunner, D. Cavalcanti, P. Skrzypczyk, T. Vertesi, Phys. Rev. Lett. 115, 190403 (2015)
[8] M. Banacki, R. Ramanathan, P. Horodecki, Multipartite channel assemblages,
arXiv:2205.05033 (2022).

Please reach out to Shmuel Friedland if you want to join the speaker for lunch or dinner, or have a meeting during their visit.

Wednesday October 11, 2023

**Geometry/Topology Seminar**

Representation Stability and Disk Configuration Spaces

Nicholas Wawrykow (University of Chicago)

3:00 PM in 636 SEO

Church-Ellenberg-Farb and Miller-Wilson proved that for a nice enough manifold X and fixed k, the k-th homology group of the ordered configuration space of points in X stabilizes in a representation-theoretic sense as the number of points in the configuration space increases. By fixing a metric on X and replacing points with open unit-diameter disks, we get a new family of configuration spaces where the geometry of X comes to the forefront. One of the simplest of these disk configuration spaces is conf(n,w), the ordered configuration space of unit-diameter disks in the infinite strip of width w. The homology groups of conf(*,w) do not stabilize in the sense of Church-Ellenberg-Farb, Miller-Wilson; however, Alpert proved that when the width is 2 they stabilize in a related sense. Alpert's methods do not extend to larger widths. In this talk I discuss various notions of representation stability, and show that when the width of the strip is at least 2, the rational homology groups of conf(*,w) stabilize in a representation-theoretic sense.

Friday October 13, 2023

Monday October 16, 2023

**Analysis and Applied Mathematics Seminar**

Moderate Deviations for Sticky Brownian Motions

Sayan Das (University of Chicago)

4:00 PM in 636 SEO

Sticky Brownian Motions are a family of correlated Brownian motions that have a tendency to stick together. They can be realized as the scaling limit of random walks in random environments and can also be viewed as random motions in a continuum-random environment. In this talk, I will present some results related to the quenched density of the motion of a particle in this continuum-random environment. In particular, I will show that under moderate deviation regime (a particular regime in between large deviation regime and diffusive regime), this quenched density after rescaling weakly converges to the solution of the stochastic heat equation with multiplicative space-time white noise. I will explain how our results shed light on the extreme behavior of Sticky Brownian Motions. This is a joint work with Hindy Drillick and Shalin Parekh.

Wednesday October 18, 2023

**Statistics and Data Science Seminar**

Flexible spatio-temporal Hawkes process models for earthquake occurrences

Junhyeon Kwon (University of North Texas)

4:00 PM in Zoom

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space–time interactions between aftershocks with a non-separable spatio-temporal triggering structure. For model estimation, we extend the model-independent stochastic declustering (MISD) algorithm and suggest substituting its histogram-based estimators with kernel methods. We demonstrate the utility of the proposed methods by applying them to the seismicity data in regions with active seismic activities.

Monday October 23, 2023

Wednesday October 25, 2023

**Dynamics Seminar**

Jordan and Cartan spectra in higher rank with applications to correlations

Mikey Chow (Yale)

4:00 PM in 427 SEO

The celebrated prime geodesic theorem for a closed hyperbolic surface says that the number of closed geodesics of length at most t is asymptotically e^t/t. For a closed surface equipped with two different hyperbolic structures, Schwartz and Sharp (’93) showed that the number of free homotopy classes of length about t in both hyperbolic structures is asymptotically a constant multiple of e^{ct} /t^{3/2} for some 0

We will discuss the asymptotic correlations of the length spectra of convex cocompact manifolds, generalizing Schwartz-Sharp's results. Surprisingly, it is helpful for us to relate this problem with understanding the Jordan spectrum of a discrete subgroup in higher rank. In particular, we will explain the source of the exponential and polynomial factors in Schwartz-Sharp's asymptotic from a higher rank viewpoint.
We will also discuss the asymptotic correlations of the displacement spectra and the ratio law between the asymptotic correlations of the length and displacement spectra.
This is joint work with Hee Oh. Monday October 30, 2023

Wednesday November 1, 2023

Friday November 3, 2023

**Departmental Colloquium**

Recent progress on the horocycle flow on strata of translation surfaces

Jon Chaika (University of Utah)

3:00 PM in 636 SEO

For about 2 decades the horocycle flow on strata of translation surfaces was studied, very successfully, in analogy with unipotent flows on homogeneous spaces, which by work of Ratner, Margulis, Dani and many others, have striking rigidity properties. In the past decade Eskin-Mirzakhani and Eskin-Mirzakhani-Mohammadi proved some analogous rigidity results for SL(2,R) and the full upper triangular subgroup on strata of translation surfaces. This talk will begin by introducing ergodic theory and translation surfaces and then it will describe some of the previously mentioned rigidity before moving onto its goal, that many such rigidity results fail for the horocycle flow on strata of translation surfaces. Time permitting we will also describe some rigidity result for special sub-objects in strata of translations surfaces. This will include joint work with Osama Khalil, John Smillie, Barak Weiss and Florent Ygouf.

Monday November 6, 2023

Wednesday November 8, 2023

Friday November 10, 2023

Monday November 13, 2023

Wednesday November 15, 2023

Monday November 20, 2023

Wednesday November 22, 2023

Monday November 27, 2023

**Analysis and Applied Mathematics Seminar**

Topological Anderson insulator by mathematical homogenization

Thuyen Dang (University of Chicago)

4:00 PM in 636 SEO

Topological insulators are materials that are insulating on the inside but are (electrically) conductive on their surface or edge. The conducting states are protected: in the presence of a defect, the transport on the edge is barely affected. This edge behavior is characterized by topological invariants of its quantization. It is known in the physics community that topological Anderson insulators (TAI) can be created by applying a disorder potential to the matter. The potential generates the phase transition of the matter that opens a spectral gap, which is the hallmark of topological insulators. In two dimensional, the TAI model can be recast as a Dirac equation. In this talk, we will discuss the formation of TAI from a mathematical homogenization point of view, and the connection between the microscopic and macroscopic Dirac operators. This is a joint work with Guillaume Bal.

Wednesday November 29, 2023

**Geometry/Topology Seminar**

Invariant subvarieties and highly transitive group actions

James Freitag (UIC)

3:00 PM in 636 SEO

Here are two rather different sounding questions: 1) Given variety V and an algebraic vector field S from V to its tangent bundle, when are there S-invariant subvarieties of V or V^n for some n?
2) Given an algebraic group acting regularly on an algebraic variety, what can you say about the group when the action is 2-transitive?
We'll explain how these two questions are intimately related through differential Galois theory. The talk won't assume anything except familiarity with classical algebraic geometry over the complex numbers.

Wednesday December 6, 2023

Friday February 2, 2024

Friday February 9, 2024

Friday February 16, 2024

Wednesday March 13, 2024

Friday April 19, 2024

**Departmental Colloquium**

TBA

Noah Giansiracusa (Bentley University)

3:00 PM in 636 SEO

TBA

Please let Laura Schaposnik at schapos@uic.edu know if you'd like to join Noah for dinner, or if you'd like to meet him during the day. He's doing a lot of interesting interdisciplinary maths: https://www.noahgian.com/