Department of

# Mathematics

Seminar Calendar
for events the week of Tuesday, October 16, 2018.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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30


Monday, October 15, 2018

3:00 pm in 345 Altgeld Hall,Monday, October 15, 2018

#### Congruence and Group Cohomology

###### Ningchuan Zhang (UIUC Math)

Abstract: In this talk, I’ll explain the relation between congruence and (continuous) group cohomology of $\mathbb{Z}_p^\times$-representations in invertible $\mathbb{Z}_p$-modules. The first half of the talk will focus on explicit computations of the two sides (including the $p=2$ case). In the second half, the connection between congruence and group cohomology will be built using the chromatic resolution (Cousin complex) of the $\mathbb{Z}_p^\times$-representations. The discussion here also applies to open subgroups of $\mathbb{Z}_p^\times$.

4:00 pm in 245 Altgeld Hall,Monday, October 15, 2018

#### Linear analysis on manifolds: the Gauss-Bonnet theorem

###### Pierre Albin   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: I'll use the Gauss-Bonnet theorem as an excuse and example to discuss linear analysis. I'll start with compact manifolds and then talk about conformally compact manifolds, a class that shows up both in conformal geometry and in physics as the setting of the AdS/CFT correspondence'.

5:00 pm in 241 Altgeld Hall,Monday, October 15, 2018

#### On Talagrand's deviation inequality for product measures

###### Pavlos Motakis (UIUC)

Abstract: We follow Ledoux's approach to deviation inequalities.

Tuesday, October 16, 2018

2:00 pm in 243 Altgeld Hall,Tuesday, October 16, 2018

#### Sampling bipartite degree sequence realizations - the Markov chain approach

###### Péter L. Erdős (A. Rényi Institute of Mathematics)

Abstract: How to analyze real life networks? There are myriads of them and usually experiments cannot be performed directly. Instead, scientists define models, fix parameters and imagine the dynamics of evolution.

Then, they build synthetic networks on this basis (one, several, all) and they want to sample them. However, there are far too many such networks. Therefore, typically, some probabilistic method is used for sampling.

We will survey one such approach, the Markov Chain Monte Carlo method, to sample realizations of given degree sequences. Some new results will be discussed.

3:00 pm in 243 Altgeld Hall,Tuesday, October 16, 2018

#### A Spectral Description of the Ruijsenaars-Schneider System

###### Matej Penciak (UIUC Math)

Abstract: The Ruijsenaars-Schneider (RS) integrable hierarchy is a many-particle system which can be viewed as a relativistic analogue of the Calogero-Moser system. The integrability and Lax form of the system has been known since it was introduced by Ruijsenaars and Schneider. In this talk I will give background on the RS system, and some classical results on elliptic functions. Then I will explain work in preparation that identifies the RS system and its Lax matrix in terms of spectral sheaves living in the total space of projective bundles on cubic curves. This work provides input to a larger project (some of it joint with David Ben-Zvi and Tom Nevins), and I will give an outline for why this spectral description will be useful in the larger project.

4:00 pm in 245 Altgeld Hall,Tuesday, October 16, 2018

#### Applications of topology for information fusion

###### Emilie Purvine (Research Scientist, Pacific Northwest National Laboratory)

Abstract: In the era of "big data" we are often overloaded with information from a variety of sources. Information fusion is important when different data sources provide information about the same phenomena. For example, news articles and social media feeds may both be providing information about current events. In order to discover a consistent world view, or a set of competing world views, we must understand how to aggregate, or "fuse", information from these different sources. In practice much of information fusion is done on an ad hoc basis, when given two or more specific data sources to fuse. For example, fusing two video feeds which have overlapping fields of view may involve coordinate transforms; merging GPS data with textual data may involve natural language processing to find locations in the text data and then projecting both sources onto a map visualization. But how does one do this in general? It turns out that the mathematics of sheaf theory, a domain within algebraic topology, provides a canonical and provably necessary language and methodology for general information fusion. In this talk I will motivate the introduction of sheaf theory through the lens of information fusion examples. This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). The views, opinions and/or findings expressed are those of the author and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government.

4:00 pm in 343 Altgeld Hall,Tuesday, October 16, 2018

###### Yijia Lin (N. Z. Snell Life Insurance Professor, University of Nebraska - Lincoln)

Abstract: In recent years, defined benefit (DB) plan sponsors have sought to reduce pension risk through strategies such as buyouts that involve the purchase of annuities from insurance companies. While pension buyouts can generally help employers reduce pension liabilities and related expenses and improve firm performance, little attention has been paid to the implications of pension risk transfer for employees. To fill this gap, we compare the total risks of employees with and without pension buyouts based on a model calibrated to market data in a stochastic framework. Our numerical examples show that the extent to which a buyout will affect the welfare of employees greatly depends on the financial soundness of their employer, plan funding status, PBGC maximum guarantees and state guarantee association protection limits. Our findings provide important insights for regulators and policymakers concerning best practices for pension de-risking through buyouts.

Yijia Lin is the N. Z. Snell Life Insurance Professor at the University of Nebraska - Lincoln. She earned BA degree in insurance and MA degree in finance and insurance both at Beijing Technology and Business University. Dr. Lin earned her Ph.D. in Risk Management and Insurance at Georgia State University. She is also a Chartered Financial Analyst (CFA®) Charterholder. Dr. Lin’s research interests are in risk management, insurance, longevity/mortality securitization and actuarial science. She has published papers in the Journal of Risk and Insurance, the North American Actuarial Journal, the Insurance: Mathematics and Economics, the Journal of Management, and others. She is also a Co-Editor of the Journal of Risk and Insurance and a Co-Editor of the North American Actuarial Journal.

Wednesday, October 17, 2018

4:00 pm in 245 Altgeld Hall,Wednesday, October 17, 2018

#### Stereotype Threat in the Classroom

###### Vanessa Rivera Quiñones (Illinois Math)

Abstract: Stereotype threat is a phenomenon in which a person’s concern about confirming a negative stereotype can lead that person to underperform. This can affect anyone, depending on the context, but students who identify with groups that are underrepresented in a field or at an institution may be especially vulnerable to its effects. Based on the book, "Whistling Vivaldi" by Claude M. Steele we will discuss what can we do to reduce the potential impact of this “threat” and to create a fair learning environment for all of our students. A limited number of copies are available to borrow. If you'd like to read the book, please contact Vanessa Rivera-Quinones (riveraq2@illinois.edu).

4:00 pm in 2 Illini Hall,Wednesday, October 17, 2018

#### Derived categories of abelian categories and applications

###### Jin Hyung To

Abstract: TBD

Thursday, October 18, 2018

11:00 am in 241 Altgeld Hall,Thursday, October 18, 2018

#### Arithmetic properties of Hurwitz numbers

###### David Hansen (University of Notre Dame)

Abstract: Hurwitz numbers are the "$\mathbf{Q}(i)$-analogue" of Bernoulli numbers; they show a remarkable number of patterns and properties, and deserve to be better-known than they are. I'll discuss some old results on these numbers due to Hurwitz and Katz, and some newer results obtained by four Columbia undergraduates during a summer REU I supervised. No background knowledge will be assumed.

12:30 pm in 464 Loomis,Thursday, October 18, 2018

#### Particle-vortex statistics and the nature of dense quark matter

###### Aleksey Cherman (INT Washington)

Abstract: Dense nuclear matter is expected to be a superfluid. Quark matter, which is expected to appear at higher densities, is also a superfluid. But quark matter turns out to be sharply distinct from a standard superfluid, because it supports Z3-valued particle-vortex braiding phases, and its effective action includes a coupling to a topological quantum field theory. Physically, our results imply that certain mesonic and baryonic excitations have orbital angular momentum quantized in units of ħ/3 in the presence of a superfluid vortex. If Z3 braiding phases and angular momentum fractionalization are absent in lower density hadronic matter, as is widely expected, then the quark matter and hadronic matter regimes of dense QCD must be separated by at least one phase transition. Since the low-density regime is a confined' phase, while the high-density regime is a `Higgs' phase due to color superconductivity, our results also have interesting implications for Higgs-confinement complementarity.

2:00 pm in 241 Altgeld Hall,Thursday, October 18, 2018

#### The Fifth Arithmetic Operation

###### Eric Wawerczyk (University of Notre Dame)

Abstract: Martin Eichler is attributed to saying: “There are five elementary operations in Number Theory: addition, subtraction, multiplication, division, and modular forms.” The point of this talk is to demonstrate a variety of amazing arithmetic formulas which can be derived using these five “basic” operations. We will be presenting amazing proofs by Euler, Riemann, and Ramanujan.

3:00 pm in 345 Altgeld Hall,Thursday, October 18, 2018

#### The $Q$-system of type $A_2^{(2)}$

###### Minyan Simon Lin (UIUC)

Abstract: In this talk, I will introduce the $Q$-system of type $A_2^{(2)}$, which is a recursion relation that is satisfied by the characters of certain finite-dimensional $\mathfrak{sl}_2$-modules. I will derive some properties of this system, such as its integrability and Laurent properties, and discuss how these properties have a natural extension to the noncommutative case. If time permits, I will discuss some of the consequences of the properties of the noncommutative $Q$-system of type $A_2^{(2)}$.

4:00 pm in 245 Altgeld Hall,Thursday, October 18, 2018

#### Resonance rigidity for Schrödinger operators

###### Tanya Christiansen (University of Missouri)

Abstract: From a mathematical point of view, resonances may provide a replacement for discrete spectral data for a class of operators with continuous spectrum. Physically, resonances may correspond to decaying waves. This talk will introduce the notion of resonances for Schrödinger operators. We discuss results, both by the speaker and others, related to the rigidity of the set of resonances of a Schrödinger operator on ${\mathbb R}^d$ with potential $V\in L^\infty_c({\mathbb R}^d)$. For example, within this class of operators, is the Schrödinger operator with $0$ potential determined by its resonances? What can we say about other sets of isoresonant potentials?

Friday, October 19, 2018

3:00 pm in 145 Altgeld Hall,Friday, October 19, 2018

#### Shadows of the Four Corner Cantor Set

###### Chi Huynh (Illinois Math)

Abstract: The set of particular interest will be $C(1/4) = C_{1/4} \times C_{1/4}$ where $C_{1/4}$ is the 1/4-Cantor set in $\mathbb{R}$. I will be presenting two proofs on the projections of $C(1/4)$ onto lines in $\mathbb{R}^2$. By utilizing the self-similar structure, these proofs present more detailed information on projections of $C(1/4)$ than the Marstrand projection theorem is able to. Due to time constraints, I will only go over one of the proofs in details, then sketch the proof of the sharper result by pointing out the necessary lemmas to obtain it.

4:00 pm in 241 Altgeld Hall,Friday, October 19, 2018