Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, October 3, 2019.

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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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Thursday, October 3, 2019

11:00 am in 241 Altgeld Hall,Thursday, October 3, 2019

#### Optimality of Tauberian theorems

###### Gregory Debruyne (Illinois & Ghent University)

Abstract: The Wiener-Ikehara and Ingham-Karamata theorems are two celebrated Tauberian theorems which are known to lead to short proofs of the prime number theorem. In this talk, we shall investigate quantified versions of these theorems and show that these are optimal. For the optimality, rather than constructing counterexamples, we shall use an attractive functional analysis argument based on the open mapping theorem. The talk is based on work in collaboration with David Seifert and Jasson Vindas.

12:00 pm in 243 Altgeld Hall,Thursday, October 3, 2019

#### Constructing pseudo-Anosov homeomorphisms using positive twists

###### Yvon Verberne (U Toronto)

Abstract: Thurston obtained the first construction of pseudo-Anosov homeomorphisms by showing the product of two parabolic elements is pseudo-Anosov. A related construction by Penner involved constructing whole semigroups of pseudo-Anosov homeomorphisms by taking appropriate compositions of Dehn twists along certain families of curves. In this talk, I will present a new construction of pseudo-Anosov homeomorphisms and discuss some of the unique properties associated to maps obtained through this new construction.

1:00 pm in 464 Loomis Laboratory ,Thursday, October 3, 2019

#### The power of string theory in TTbar and related theories

###### David Kutasov (University of Chicago Physics)

Abstract: I describe the recent discovery of a class of non-local field theories that can be thought of as irrelevant deformations of two dimensional conformal field theories, focusing on their description as deformations of string theory on three dimensional anti-de-Sitter space.

2:00 pm in 347 Altgeld Hall,Thursday, October 3, 2019

#### Introduction to Spin Glasses Part I

###### Qiang Wu (UIUC Math)

Abstract: I will introduce some spin glass models in the first talk, such as Curie-Weiss(CW) model, Sherrington-Kirkpatrick(SK) model etc, then particularly discuss the high temperature analysis of SK model by Guerra’s interpolation.

3:00 pm in 347 Altgeld Hall,Thursday, October 3, 2019

#### Plabic R-Matrices

###### Sunita Chepuri   [email] (University of Minnesota, Twin Cities)

Abstract: Postnikov's plabic graphs in a disk are used to parametrize totally nonnegative Grassmannians. One of the key features of this theory is that if a plabic graph is reduced, the face weights can be uniquely recovered from boundary measurements. On surfaces more complicated than a disk this property is lost. In this talk, we investigate a certain semi-local transformation of weights for plabic networks on a cylinder that preserves boundary measurements. We call this a plabic R-matrix. We explore the properties of the plabic R-matrix, including the symmetric group action it induces on plabic networks and its underlying cluster algebra structure.

4:00 pm in 245 Altgeld Hall,Thursday, October 3, 2019

#### The Rise of Peer-to-Peer Insurance and Its Mathematical Modeling

###### Runhuan Feng   [email] (University of Illinois at Urbana-Champaign)

Abstract: Peer-to-peer (P2P) insurance is a decentralized network in which participants pool their resources together to compensate those who suffer losses. It is a revival of a centuries-old practice in many ancient societies where members care for each other’s financial needs in the event of misfortune. With the aid of internet technology, P2P insurance is becoming a transparent, high-tech and low-cost alternative to traditional insurance and is viewed by many as a huge disruptor to the traditional insurance industry in the same way Uber is to the taxi industry. P2P insurance took an unexpected twist in the Chinese market. A new business model called “mutual aid” is largely driven by many non-insurance tech firms, including the e-commerce giant, Alibaba. In less than three years, the mutual aid industry amassed close to 260 million participants, which is nearly 20% of the Chinese population, or equivalently, 80% of the US population. Such an unprecedented development is causing huge anxiety for insurers and regulators in China and being closely watched by their peers around the world. Despite the fast-changing landscape in this field, there has no previous academic literature for the theoretical underpinning of P2P insurance. Our research team presents the first such effort to build the mathematical framework under which the design, engineering and management of mutual aid and P2P insurance can be studied. This presentation is based on joint work with Samal Abdikerimova and Chongda Liu.