Department of

Mathematics


Seminar Calendar
for Mathematics in Science and Society events the year of Tuesday, March 13, 2018.

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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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Tuesday, February 6, 2018

4:00 pm in 314 Altgeld Hall,Tuesday, February 6, 2018

Fighting Gerrymandering with the Blue Waters Supercomputer

Wendy K. Tam Cho (Dept of Political Science, Illinois)

Abstract: Important insights into redistricting can be gained through an interdisciplinary approach that combines research from many fields, including statistics, operations research, computer science, high performance computing, math, law, and political science. Our work integrates insights from all of these disciplines to create a novel approach for analyzing and reforming redistricting in a way that is tightly coupled with the framework that the Supreme Court has outlined over the past 5 decades.

Wendy K. Tam Cho is Professor in the Departments of Political Science, Statistics, Asian American Studies, and the College of Law, Senior Research Scientist at the National Center for Supercomputing Applications, a Guggenheim Fellow, Faculty in the Illinois Informatics Institute, and Affiliate of the Cline Center for Democracy, the CyberGIS Center for Advanced Digital and Spatial Studies, the Computational Science and Engineering Program, and the Program on Law, Behavior, and Social Science, at the University of Illinois at Urbana-Champaign. She also founded and teaches at the Champaign-Urbana Math Circle.

Her research on redistricting has been published in many scholarly fields, including operations research, computer science, high performance computing, political science, and law. Its premise as a standard for adjudicating partisan gerrymandering was the subject of 11 amicus briefs and was presented in oral arguments before the Supreme Court.

Tuesday, March 13, 2018

4:00 pm in 245 Altgeld Hall,Tuesday, March 13, 2018

Fields Medal Confidential: Behind the scenes of mathematicians’ most famous prize, 1936-1966

Michael J. Barany (Dartmouth College)

Abstract: First presented in 1936, the Fields Medal quickly became one of mathematicians' most prestigious, famous, and in some cases notorious prizes. Because its deliberations are confidential, we know very little about the early Fields Medals: how winners were selected, who else was considered, what values and priorities were debated---all these have remained locked in hidden correspondence. Until now. My talk will analyze newly discovered letters from the 1950 and 1958 Fields Medal committees, which I claim demand a significant change to our understanding of the first three decades of medals. I will show, in particular, that the award was not considered a prize for the very best mathematicians, or even for the very best young mathematicians. Debates from those years also shed new light on how the age limit of 40 came about, and what consequences this had for the Medal and for the mathematics profession. I argue that 1966 was the turning point that set the course for the Fields Medal's more recent meaning.

Tuesday, September 18, 2018

4:00 pm in 245 Altgeld Hall ,Tuesday, September 18, 2018

Möbius kaleidocycles: a new class of everting ring linkages

Eliot Fried (Mathematics, Mechanics, and Materials Unit, Okinawa Institute of Science and Technology Graduate University)

Abstract: Many of Escher’s works have become mainstays of popular culture. Famous examples include his Möbius bands and kaleidocycles. Made from six identical regular tetrahedra joined by revolute hinges, a kaleidocycle possesses a single internal degree-of-freedom that is manifested by a cyclic everting motion that brings different faces of the tetrahedra into view. We will describe "Möbius Kaleidocycles," a previously undiscovered class ring linkages made from seven or more identical links joined by revolute hinges. For each number of links, there exists a specific twist angle between neighboring hinges for which the associated Möbius Kaleidocycle possesses only a single internal degree-of-freedom, allowing for cyclic eversion, and the hinge orientations induce a nonorientable topology equivalent to that of a 3π twist Möbius band. Apart from technological applications, including perhaps the design of new organic ring molecules with peculiar electronic properties, Möbius kaleidocycles generate a myriad of intriguing questions in geometry and topology, some of which will be addressed in this talk. This is joint work with postdoctoral scholar Johannes Schönke.

Tuesday, October 16, 2018

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.

Tuesday, October 23, 2018

4:00 pm in 245 Altgeld Hall,Tuesday, October 23, 2018

Multi-scale mathematical models of disease

Reinhard C. Laubenbacher (University of Connecticut School of Medicine and Jackson Laboratory for Genomic Medicine)

Abstract: Multi-scale mathematical and computational modeling has emerged as a key technology in many areas of engineering, manufacturing, and business. It also holds great promise for biomedicine, with a wide range of potential applications. For instance, well-validated mathematical models could help limit the use of animal experiments for drug discovery or develop better-optimized treatment protocols for patients. Unique challenges arise in this context, however, such as the existence of feedback loops between scales, e.g., the bidirectional interplay between processes at the organism and intracellular levels, or the lack of knowledge about physical or biochemical principles underlying disease mechanisms. In particular, this raises challenging mathematical problems, such as analysis and validation of the dynamics of complex hybrid models. It also complicates the application of optimal control techniques, which is of particular importance, since most problems in biomedicine ultimately are about control. These issues will be illustrated through two ongoing case studies, metabolic drivers of tumor growth and the immune response to respiratory fungal infections.

Dr. Laubenbacher joined the University of Connecticut Health Center in May 2013 as Professor in the Department of Cell Biology and Co-Director of the Center for Quantitative Medicine. Prior to this appointment, he served as a Professor at the Virginia Bioinformatics Institute and a Professor in the Department of Mathematics at Virginia Tech since 2001. He was also an Adjunct Professor in the Department of Cancer Biology at Wake Forest University in Winston-Salem (NC) and Affiliate Faculty in the Virginia Tech Wake Forest University School of Biomedical Engineering and Sciences. In addition, Dr. Laubenbacher was also Professor of Mathematics at New Mexico State University. He has served as Visiting Faculty at Los Alamos National Laboratories, was a member of the Mathematical Science Research Institute at Berkeley in 1998, and was a Visiting Associate Professor at Cornell University in 1990 and 1993. Current interests in Dr. Laubenbacher’s research group include the development of mathematical algorithms and their application to problems in systems biology, in particular the modeling and simulation of molecular networks. An application area of particular interest is cancer systems biology, especially the role of iron metabolism in breast cancer.