# Pi Mu Epsilon Conference

# April 3–4, 2020 (Conference Cancelled)

Peter Engel Science Center

Saint John's University (please park in Parking Lot P2 or P4)

## Invited Speaker: Dr. Jesús De Loera (University of California, Davis)

Biography (source): Jesús De Loera was born and raised in Mexico City. He received his Bachelor of Science degree in Mathematics from the National University of Mexico in 1989, a M.A. in Mathematics from Western Michigan in 1990, and a Ph.D in Applied Mathematics from Cornell University in 1995. He arrived at UC Davis in 1999, where he is now a professor of Mathematics as well as a member of the Graduate groups in Computer Science and Applied Mathematics. He has held visiting positions at the University of Minnesota, the Swiss Federal Technology Institute (ETH Zürich), the Mathematical Science Institute at Berkeley (MSRI), Universität Magdeburg (Germany), the Institute for Pure and Applied Mathematics at UCLA (IPAM), the Newton Institute of Cambridge Univ. (UK), and the Technische Universität München. He has taught courses at universities in the USA, Mexico, Germany and Switzerland.

He is an expert in the field of Discrete Mathematics, but his research encompasses a diverse set of topics including his work in (pure) Convex Geometry, Algebraic Combinatorics, and Combinatorial Commutative Algebra, as well as his (applied) work in Combinatorial Optimization and Algorithms. In addition to more than 80 published research papers, he has co-written two graduate level textbooks: "*Triangulations: Structures for Algorithms and Applications''* (Springer, with J. Rambau and F. Santos) and *`"Algebraic and Geometric Ideas in the Theory of Discrete Optimization''* (SIAM, with R. Hemmecke and M. Koeppe). The first being a treatise about combinatorics of triangulations of polytopes and the second an introduction to the state of the art in algebraic-geometric algorithms in optimization.

In general, he enjoys rethinking Mathematics in terms of algorithmic questions and understanding how computers can be "taught'' to discover or prove theorems (e.g., automatically produce rational generating functions from geometric counting questions). He approaches difficult computational problems using tools from Algebra, Combinatorics, and Convex Geometry, and Topology. He believes in the exciting future of interdisciplinary work. Some of his favorite mathematical objects are *polytopes*, which are multidimensional generalizations of polygons and cubes (some pretty ones seen in the pictures above).

His research has been recognized in several ways. He was awarded an Alexander von Humboldt Fellowship in 2004, the 2010 INFORMS computer society prize, a 2013 John von Neumann professorship at the Technical University of Munich and he was elected as a fellow of the American Mathematical Society (AMS) in 2014 and in 2019 he became a fellow of the Society of Industrial and Applied Mathematics (SIAM). He has been plenary or semi-plenary speaker at many major scientific conferences including, the Joint Math Meetings, SIAM annual meeting, MAA Mathfest, AMS and MAA regional meetings, COMBINATEXAS, CANADAM, FPSAC and MOPTA. He has presented more than 80 invited scientific colloquia in well-known academic institutions such as MIT, Caltech, Oxford Univ., UC Berkeley, UCLA, Cambridge Univ., MAA Carriage House, Claremont-McKenna College, IBM, and Courant Institute NYU. He has also given more than 100 seminars at academic departments around the world. He has received many national and international grants to support his work, including from NSF, NSA, CONACYT, and IBM.

He is an associate editor of the journals "SIAM Journal of Discrete Mathematics'', "SIAM journal of Applied Algebra and Geometry'', "Boletin de la Sociedad Matematica Mexicana'' and a former editor of "Discrete Optimization''. He has also served the mathematics community as member of in many committees and organizer of many events, with an emphasis in promoting mathematics for underserved communities. E.g, recently he served in the AMS committee of Education, as well as Vice-Chair of the UC Davis Mathematics Department and Faculty Assistant to the Dean of Mathematical and Physical Sciences in undergraduate matters. He was elected to the AMS executive council in 2015 and has coorganized over 30 workshops and events, from many small regional meetings (e.g. AMS meetings) to two large semester-long MSRI programs "Discrete and Computational Geometry'' (2003) and ``Geometric and Topological Combinatorics (2017). He is currently in the Scientific board of ICERM and AIM.

For his dedication to outstanding mentoring and teaching he received the 2003 UC Davis Chancellor's fellow award, the 2006 UC Davis award for diversity, the 2007 Award for excellence in Service to Graduate students by the UC Davis graduate student association, the 2013 Chancellor's award for mentoring undergraduate research. In 2017, the Mathematical Association of America Golden Section Award and in 2018 he won the UC Davis College of Letters and Science Distinguished Teaching Award. He has successfully supervised fourteen Ph.D students, eight postdoctoral scholars, and over 50 undergraduates doing research projects. He is very proud of all the hundreds of successful students who have shared mathematics with him over the years.

### 2020 PME Schedule and Abstracts:

**Friday, April 3, 8:30pm - Pellegrene Auditorium.**

**Title**: Geometric/Topological problems arising in Artificial Intelligence and Data Science

**Abstract:** Today, the enhanced ability to observe, collect, and store data in the sciences, in commerce, in medicine, and many other fields as well as the increased numbers of connections (e.g., emergence of smart-phones and social networks as central aspects of our daily life) calls for a change in our understanding of data and information. Increasingly mathematicians of the future will try to understand and extract usable information from massive data arising in applications and within mathematics itself, looking more and more like experimental scientists who collect data to explore conjectures and patterns. But the most exciting part is perhaps the new types of mathematics that will have to be developed. My lecture will focus on how geometry and topology are increasingly playing a role in understanding the shape of data. No priorknowledge of these topics will be assumed.

**Saturday, April 4, 10:30am - Pellegrene Auditorium.**

**Title:** Algebraic and Geometric methods in Modern Optimization

**Abstract:** Optimization is a vibrant growing area of Applied Mathematics. Its many successful applications depend on efficient algorithms and this has pushed the development of theory and software. In recent years there has been a resurgence of interest to use \non-standard" techniques to estimate the complexity of computation and to guide algorithm design. New interactions with fields like algebraic geometry, representation theory, number theory, combinatorial topology, algebraic combinatorics, and convex analysis have contributed non-trivially to the foundations of computational optimization. I will try to give a taste of these new approaches. Most of my time I will focus on the simplest and very useful problem of minimizing a linear function over a region defined by linear inequalities and equation constraints (linear programming!) and describe how \non-traditional" thinking shines new light on the computational methods.

**Upcoming Conference Speakers **

- 2020 Dr. Jesús De Loera

**Former Conference Speakers**

- 2019 Dr. Talitha Washington
- 2018 Tim Chartier
- 2017 Francis Su
- 2016 Judy Walker
- 2015 Ami Radunskaya
- 2014 Hal Schenck
- 2013 Annalisa Crannell (Videos: Friday's Lecture, Saturday's Lecture)
- 2012 Kenneth Millett
- 2011 William Dunham
- 2010 Claudia Neuhauser
- 2009 Joe Gallian
- 2008 (Conference cancelled due to weather)
- 2007 Carlos Castillo-Chavez
- 2006 Edward Burger
- 2005 Jennifer Quinn
- 2004 Frank Farris
- 2003 Colin Adams
- 2002 David Bressoud
- 2001 Underwood Dudley
- 2000 Sam Patterson
- 1999 Robert L. Devaney
- 1998 Richard Guy
- 1997 Ron Graham
- 1996 Frank Morgan
- 1995 Carl Pomerance
- 1994 Philip Straffin
- 1993 Thomas Banchoff
- 1992 Judith Grabiner
- 1991 Raymond Smullyan
- 1990 Joan Hutchinson
- 1989 Richard Askey
- 1988 Sherman Stein
- 1987 Reuben Hersh
- 1986 Peter Hilton
- 1985 I.N. Herstein
- 1984 Ruth Struik
- 1983 Joan Fisher Box, George Box
- 1982 Alfred Willcox (in conjunction with the North Central Section Meeting)
- 1981 Doris Schattschneider, Leonard Gillman, Don Koehler
- 1980 Mary Ellen Rudin
- 1979 Paul Halmos

**Lectures will be geared toward a general audience**

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