Department of

# Mathematics

Seminar Calendar
for events the day 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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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