Seminar Calendar
for events the week of Monday, January 23, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, January 23, 2017

Symplectic and Poisson Geometry Seminar
4:00 pm   in 243 Altgeld Hall,  Monday, January 23, 2017
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Submitted by icontrer.
Ely Kerman (UIUC)
J-holomorphic cylinders between ellipsoids
Abstract: The primary tool for detecting obstructions to symplectic embeddings are regular J-holomorphic curves in symplectic cobordisms. The more the better. In this talk, I will describe an existence theorem for such curves in dimension 4 and, time permitting, an application. This is based on joint work in progress with Richard Hind.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, January 23, 2017
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Submitted by laugesen.
Bruce Reznick (Department of Mathematics, University of Illinois)
Problem-solving, question-asking and knowledge-finding
Abstract: Three of the most important activities that researchers perform are listed in the title. I will talk about practical techniques for improving your skills in these areas, using specific examples of mathematics from my own work and the work of my graduate students. My intention that most members of the audience will see at least a few objects which resonate with their own mathematical interests.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, January 23, 2017
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Submitted by mjunge.
Ed McDanoald (NSW)
Quantised Calculus in One Dimension and Applications
Abstract: This talk will give some introduction for certain topics in noncommutative geometry with special emphasis on the 1-dimensional torus. An organizational meeting will be held a week later.

Tuesday, January 24, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by clein.
Sarah Mousley (Illinois Math)
Boundary maps for some hierarchically hyperbolic spaces
Abstract: There are natural embeddings of right-angled Artin groups $G$ into the mapping class group $Mod(S)$ of a surface $S$. The groups $G$ and $Mod(S)$ can each be equipped with a geometric structure called a hierarchically hyperbolic space (HHS) structure, and there is a notion of a boundary for such spaces. In this talk, we will explore the following question: does an embedding $\phi: G \rightarrow Mod(S)$ extend continuously to a boundary map $\partial G \rightarrow \partial Mod(S)$? That is, given two sequences $(g_n)$ and $(h_n)$ in $G$ that limit to the same point in $\partial G$, do $(\phi(g_n))$ and $(\phi(h_n))$ limit to the same point in $\partial Mod(S)$? No background in HHS structures is needed.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by anush.
Evgeny Gordon (Eastern Illinois Math)
Will the Nonstandard Analysis become the Analysis of Future?
Abstract: In 1973 Abraham Robinson gave a talk about the nonstandard analysis (NSA) at the Institute for Advanced Study. After his talk Kurt G\"odel made a comment, in which he predicted that "...there are good reasons to believe that Non-Standard Analysis in some version or other will be the analysis of the future". One has to admit that during the fifty years since this prediction, it did not come true. One of the reasons is that the most part of researchers in NSA considered it as a tool of obtaining new results in standard mathematics, instead of consider it as a more appropriate language, in which the "book of nature is written". Nowadays, the investigation of DE's that simulate processes in science and economy are based on computer (discrete) simulations of these DE's.
  In this talk I will try to justify the point of view that the language of NSA is more appropriate for investigation of the interaction between continuous models and their discrete simulations (or maybe vise versa - between discrete models and their continuous simulation, according to a popular among applied mathematicians point of view). The reason is that not well defined properties ("very big", "very small", "far enough of the boundaries of computer memory", etc.) can be introduced in the language of NSA on the level of rigor of Cantor's Set Theory. I will discuss some NSA theorems in algebra, calculus, ergodic theorem and quantum mechanics) concerning this problem that have intuitively clear sense and agree with computer experiments, while their formulation in the language of standard mathematics looks irrelevant and sometimes even unreadable.

Graduate Student Number Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by amalik10.
Byron Heersink (UIUC)
Poincar\'e sections for the horocycle flow in covers of SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) and applications to Farey fraction statistics
Abstract: For a given finite index subgroup $H\subseteq$SL(2,$\mathbb{Z}$), we use a process developed by Fisher and Schmidt to lift a Poincar\'e section of the horocycle flow on SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$) found by Athreya and Cheung to the finite cover SL(2,$\mathbb{R}$)/$H$ of SL(2,$\mathbb{R}$)/SL(2,$\mathbb{Z}$). We then relate the properties of this section to the gaps in Farey fractions and describe how the ergodic properties of the horocycle flow can be used to obtain certain statistical properties of various subsets of Farey fractions.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by katz.
Yungfeng Jiang (U Kansas Math)
On the Behrend function and its motivic version in Donaldson-Thomas theory
Abstract: The Behrend function, introduced by K. Behrend, is a fundamental tool in the study of Donaldson-Thomas invariants. In his foundational paper K. Behrend proves that the weighted Euler characteristic of the Donaldson-Thomas moduli space weighted by the Behrend function is the Donaldson-Thomas invariants defined by R. Thomas using virtual fundamental cycles. This makes the Donaldson-Thomas invariants motivic. In this talk I will talk about the basic notion of the Behrend function and apply it to several other interesting geometries. If time permits, I will also talk about the motivic version of the Behrend function and the famous Joyce-Song formula of the Behrend function identities.

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 24, 2017
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Submitted by seminar.
Daniel Linders (Technical University of Munich)
A New Approach for Buffering Portfolio Returns in Investment-Linked Annuities
Abstract: This paper introduces a new class of investment-linked annuity contracts. To reduce payout volatility, we gradually adjust cash flows to portfolio returns. This contrasts with standard investment-linked annuity contracts in which cash flows immediately incorporate portfolio returns. To build a realistic risk-management framework, we consider a general financial market. Our framework allows to use various non-Gaussian distributions which incorporate stylized facts about portfolio returns. Furthermore, we show how to price and hedge the liabilities of our new annuity contract.

Graduate Student Analysis Seminar
4:00 pm   in 131 English Building,  Tuesday, January 24, 2017
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Submitted by compaan2.
(UIUC Math)
Organizational Meeting
Abstract: A brief meeting to schedule speakers for the semester.

Wednesday, January 25, 2017

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Wednesday, January 25, 2017
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Submitted by seminar.
Jing Wang (J.L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign)
Degenerate diffusions and heat kernel estimates
Abstract: In this talk we will look at degenerate hypoelliptic diffusion processes and the small time behaviors of their transition densities. Diffusion processes play important roles in modeling risky assets in financial mathematics and actuarial science. The small time estimates of their transition densities are particularly useful for pricing options with short maturities. In this talk we will introduce the degenerate diffusion processes that are characterized by their levels of degeneracy. The ones of weaker degeneracy -- also called strong Hörmander's type -- are closely related to sub-Riemannian geometry. An important example is the Brownian motion process on a sub-Riemannian manifold. In general, small time asymptotic estimates are available for a subelliptic heat kernel on the diagonal and out of cut-locus. In special cases such as for Brownian motions on sub-Riemannian model spaces, we can obtain explicit expressions for their transition densities (heat kernels) and hence small time asymptotic estimates, particularly on the cut-loci. In the second part of the talk, we will study the strictly degenerate case-diffusion processes that are of weak Hörmander's type. Namely the hypoellipticity is fulfilled with the help of the drift term. This type of processes are particularly interesting in financial mathematics for pricing Asian options. We obtain large deviation properties for nilpotent diffusion processes of weak Hörmander's type.

IGL Outreach Information Session
5:15 pm   in 245 Altgeld Hall,  Wednesday, January 25, 2017
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Submitted by emerrim2.
  [email]IGL Outreach Information Session
Abstract: Come learn about activities the Illinois Geometry Lab runs in the local community throughout the year, and how to get involved!

Thursday, January 26, 2017

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, January 26, 2017
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Submitted by mastroe2.
Organizational Meeting

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Thursday, January 26, 2017
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Submitted by seminar.
Colin Ramsay (University of Nebraska - Lincoln)
Exploring the Optimal Design of an Employer Sponsored Sickness-Disability Compensation Insurance Plan When Sickness Presenteeism Is Penalized
Abstract: We explore some aspects of the moral hazard issues (presenteeism, absenteeism, and shirking) on the optimal design of a 100% employer sponsored sickness-disability compensation insurance plan when the employer penalizes sickness presenteeism. For simplicity we assume employees experience no mortality but can become sick. Specifically, we assume an employee’s health follows a simple multi-state model with a “severely ill” sickness state where employees are symptomatic, i.e., they show signs of illness while at work, and presenteeism clearly exists. To combat absenteeism, the employer may randomly verify an employee’s claim of sickness. However, to combat presenteeism, we also introduce the new concept of a presenteeism penalty whereby employees who are found to be very sick while at work (and thus have low productivity) are sent home and receive a penalized sick-pay that is lower than the normal sick pay. Thus sick employees must decide whether to stay at home and receive a sick pay (that is less than their working pay) or go to work sick and run the risk of being sent home and penalized. We assume employees are risk averse utility maximizers and each employee has one of eight strategies for staying home or working while sick that maximizes her lifetime expected discounted utility. For each employee strategy, Volterra integral equations are used to derive expressions for an employee’s lifetime expected discounted utility and the employer’s expected discounted accounting profits. Laplace transforms are used to derive asymptotic expressions for the solutions to these integral equations. To explore the optimal design, we focus on four primary plan design factors: sick pay, the presenteeism penalty, and two health check probabilities. These plan design factors have a direct impact an employee’s lifetime expected discounted utility and the employer’s profits over an employee’s working lifetime. The primary plan design factors are used as parameters in the asymptotic solutions to explore their impact on the optimal sickness compensation insurance plan. Using a hypothetical example, we found that shirking is very rarely a problem and that the employer’s profit is maximized when very sick employees are encouraged to stay home. Based on a joint work with Prof. Victor I. Oguledo and Ms. Annika Krutto.

Friday, January 27, 2017

Graduate Geometry/Topology Seminar
4:00 pm   in 241 Altgeld Hall,  Friday, January 27, 2017
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Submitted by dcarmod2.
Daniel Carmody (UIUC Math)
Galois Categories and the Topological Galois Correspondence
Abstract: Classical Galois theory for fields gives a correspondence between closed subgroups of the Galois group of a Galois extension and intermediate subfields. The theory of covering spaces in topology gives a correspondence between connected coverings of nice spaces and subgroups of the fundamental group. The purpose of this talk is to explain the relationship between (and generalization) of these two theorems.

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, January 27, 2017
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Submitted by anush.
Anush Tserunyan (UIUC Math)
On "Structurable equivalence relations" by R. Chen and A. Kechris: Introduction
Abstract: For a class $\mathcal{K}$ of countable relational structures, a countable Borel equivalence relation $E$ is said to be $\mathcal{K}$-structurable if there is a Borel way to put a structure from $\mathcal{K}$ on each $E$-equivalence class. The paper of Chen and Kechris [arXiv link] studies the global structure (including Borel homomorphisms and reductions) of the classes of $\mathcal{K}$-structurable equivalence relations for various $\mathcal{K}$. In this introductory talk, we will give some background and survey the main results of the paper.

Saturday, January 28, 2017

Gathering for Gardner
2:00 pm   in Altgeld Hall,  Saturday, January 28, 2017
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Submitted by seminar.
Gathering for Gardner
Abstract: The Department of Mathematics at the University of Illinois at Urbana-Champaign would like to invite you to our winter math carnival! Gathering for Gardner will be held on Saturday, January 28, 2017 from 2 - 5 pm in Altgeld Hall. This fun filled day will be packed with hands on activities, demonstrations, games and puzzles, refreshments, and mathematical prizes for participants! We will have activities for members of the public of all ages. More information is available at http://www.math.uiuc.edu/~lanius2/G4G.html