Difference between revisions of "Colloquia"

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(Alejandra Quintos abstract)
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==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison) ==
 
==September 30, 2022, Friday at 4pm [https://alejandraquintos.com/ Alejandra Quintos] (University of Wisconsin-Madison) ==
 
(host: Stovall)
 
(host: Stovall)
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'''Dependent Stopping Times and an Application to Credit Risk Theory'''
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Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.
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In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.
 
==October 7, 2022, Friday at 4pm  [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==
 
==October 7, 2022, Friday at 4pm  [https://www.daniellitt.com/ Daniel Litt] (University of Toronto)==
 
(host: Ananth Shankar)
 
(host: Ananth Shankar)

Revision as of 05:37, 21 September 2022


In 2022-2023, our colloquia will be in-person talks in B239 unless otherwise stated.

September 9 , 2022, Friday at 4pm Jing Tao (University of Oklahoma)

(host: Dymarz, Uyanik, WIMAW)

On surface homeomorphisms

In the 1970s, Thurston generalized the classification of self-maps of the torus to surfaces of higher genus, thus completing the work initiated by Nielsen. This is known as the Nielsen-Thurston Classification Theorem. Over the years, many alternative proofs have been obtained, using different aspects of surface theory. In this talk, I will overview the classical theory and sketch the ideas of a new proof, one that offers new insights into the hyperbolic geometry of surfaces. This is joint work with Camille Horbez.

September 23, 2022, Friday at 4pm Pablo Shmerkin (University of British Columbia)

(host: Guo, Seeger)

Incidences and line counting: from the discrete to the fractal setting

How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the continuum setting, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.

September 30, 2022, Friday at 4pm Alejandra Quintos (University of Wisconsin-Madison)

(host: Stovall)

Dependent Stopping Times and an Application to Credit Risk Theory

Stopping times are used in applications to model random arrivals. A standard assumption in many models is that the stopping times are conditionally independent, given an underlying filtration. This is a widely useful assumption, but there are circumstances where it seems to be unnecessarily strong. In the first part of the talk, we use a modified Cox construction, along with the bivariate exponential introduced by Marshall & Olkin (1967), to create a family of stopping times, which are not necessarily conditionally independent, allowing for a positive probability for them to be equal. We also present a series of results exploring the special properties of this construction.

In the second part of the talk, we present an application of our model to Credit Risk. We characterize the probability of a market failure which is defined as the default of two or more globally systemically important banks (G-SIBs) in a small interval of time. The default probabilities of the G-SIBs are correlated through the possible existence of a market-wide stress event. We derive various theorems related to market failure probabilities, such as the probability of a catastrophic market failure, the impact of increasing the number of G-SIBs in an economy, and the impact of changing the initial conditions of the economy's state variables. We also show that if there are too many G-SIBs, a market failure is inevitable, i.e., the probability of a market failure tends to one as the number of G-SIBs tends to infinity.

October 7, 2022, Friday at 4pm Daniel Litt (University of Toronto)

(host: Ananth Shankar)

October 14, 2022, Friday at 4pm Andrew Sageman-Furnas (North Carolina State)

(host: Mari-Beffa)

October 21, 2022, Friday at 4pm Ngoc Mai Tran (Texas)

(host: Rodriguez)

November 7-9, 2022, Kristen Lauter (Facebook)

Distinguished lectures

(host: Yang).

November 11, 2022, Friday at 4pm Joel Tropp (Caltech)

This is the Annual LAA lecture. See this for its history.

(host: Qin, Jordan)

November 18, 2022, Friday at 4pm [TBD]

(reserved by HC. contact: Stechmann)

December 2, 2022, Friday at 4pm [TBD]

(reserved by HC. contact: Stechmann)

December 9, 2022, Friday at 4pm [TBD]

(reserved by HC. contact: Stechmann)

Future Colloquia

Fall 2022

Spring 2023

Past Colloquia

Spring 2022

Fall 2021

Spring 2021

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

WIMAW