Title: Inequalities in Topology Motivated by the Schwarz Lemma
Abstract: We will discuss a number of inequalities that can be stated in purely topological terms, but their proofs may involve other ideas. The protoptype is Knesers inequality for the degree of a map of Riemann surfaces, published in 1930: if X, Y are Riemann surfaces of genus (gX,gY) > 1 and f : X → Y is a continuous map, then |degree(f)| ≤ (gX − 1)/(gY − 1). If X, Y have complex structures and f is holomorphic, then the inequality would be an immediate consequence of the Schwarz Lemma: holomorphic maps of the unit disk do not increase length in the Poincaré metric. We will discuss proofs of this inequality and related ones by various methods: bounded cohomology, harmonic maps, Higgs bundles. We will also indicate, as time permits, how these inequalities have motivated much work on the structure of the space of representations of the fundamental group of a surface in various Lie groups. This will be an exposition of work of Milnor, Wood, Dupont, Goldman, Gromov, Hitchin, and many others. It should be mentioned that some of the current work on this subject uses Ahlfors generalization of the Schwarz Lemma in a very essential way.
Date and time: Tuesday, January 16 at 4:00 in room 135 TMCB.
The vast majority of mathematical puzzles ask for the existence of a solution. It is merely an exercise when the method is known and it is more of a puzzle when the method is not clear. An algorithmic puzzle takes this further by only asking for the method itself or a property of the method. It is in this sense that much of computer science is puzzle solving. We discuss the theory behind this in the context of material taken from Martin Gardner’s Scientific American column. The answer to the following puzzle will be given:
There are five pirates dividing up 100 gold coins. Pirates are strictly ordered by seniority, are very logical and wish to live. The rule pirates use to divide gold is: (1) the most senior pirate suggests a division, (2) all pirates vote on it, (3) if at least half vote for it then it is done, otherwise the senior pirate is killed and the process starts over. What happens?
Dana Richards is an associate professor of Computer Science at George Mason University. His research is on theoretical and algorithmic topics. He has been a friend of Martin Gardner for nearly four decades and has edited Gardner’s book
The Colossal Book of Short Puzzles and Problems.
Join us at 4:00 on March 22nd to hear from Dana in 1170 TMCB.
Date: April 12th, 2018 4:00 PM 1170 TMCB
Title: Frosting Fairness, Finally!
Abstract: Many of us are familiar with how to slice a cake ensuring equal sized slices for all. But what about those of us who want an equal amount of frosting as well?! This question is a classic with the problem solvers amongst us. In 1975, Martin Gardner considered a square cake cut into 7 pieces in his Scientific American column. More than a decade earlier, H.S.M. Coxeter posed the problem for a square cake sliced into 9 pieces as an exercise in his book, Introduction to Geometry. Together, we will solve this problem for a square cake cut into 5 pieces, and investigate the other cake shapes for which the same procedure will produce slices with equal cake and frosting.
Bio: Alissa S. Crans has been recognized nationally for her enthusiastic ability to share and communicate mathematics, having been honored by the MAA with the Hasse Prize and Alder Award. Her research lies in the field of higher-dimensional algebra and is currently supported by a Simons Foundation Collaboration Grant. Alissa is known for her active mentoring of women and underrepresented students, as well as of junior faculty as a member of the MAA Project NExT leadership team. When not enticing students with the beauty of mathematics at Loyola Marymount University or sharing her enthusiasm for math in settings ranging from “Nerd Night Los Angeles” to public school classrooms, you can find her rehearsing with the Santa Monica College Wind Ensemble or on her quest to find the spiciest salsa in LA.
Come hear from Mason Victors, Director of Data Science at Recursion Pharmaceuticals. The event will be held in TMCB 1170 at 4:30 on December 14th. Refreshments will be served.
Adam Rich of Beasley Insurance will discus ways that math is used in his career. The event will take place on December 7th 2017 in TMCB 1170 at 4:30PM. Refreshments will be served.
The Alexander Grothendieck Lecture
Title: Modular Representation theory (the wild world of characteristic p)
Tuesday, December 5 4:00 PM 135 TMCB
Abstract: Strange examples arise when we look at actions on vector spaces over a field of charactersitic p > 0. Classically, one considers transformation groups acting on real vector spaces and uses Lie algebras to study continuous actions. Motivated by number theory and algebraic geometry, one also studies actions on vector spaces over other fields. Surprising behavior occurs and there are more strange examples than general theory.
Refreshments served at 3:30 in 294 TMCB
Michael Dorff, Mathematics Department Chair, will discuss how mathematics is making Hollywood better. Join us Thursday, November 30th, at 4:30 im TMCB 1170. Refreshments will be served.
The college of physical and mathematical sciences student alumni networking dinner is Thursday, November 16th at 6:30 PM in the Hinckley Center 3rd Floor Assembly Hall. Please RSVP at TinyURL.com/cpmsnetworkingdinner
Title: From Science to Product at AncestryDNA
Abstract: Converting cutting-edge research into everyday consumer products is exciting and challenging. In this talk I will discuss recent groundbreaking research (published in Nature Communications) that identifies recent populations using genetic data from our direct to consumer DNA business. Then, I will highlight some of the process that went into turning that research into a product that helps users connect with recent populations their ancestors may have come from.
Biography: Ross Curtis joined the AncestryDNA team in January of 2012. He is a computational biologist specializing in genetics and visual analytics and loves applying his expertise to family history and genealogy. Before AncestryDNA, Dr. Curtis focused on using visualization and statistics to discover genetic mutations that contribute to disease. Dr. Curtis received his B.S. from Brigham Young University and his Ph.D. in Computational Biology from Carnegie Mellon University.
Join us Thursday, November 16 at 4:30 in TMCB 1170 to hear about Ross’ experience on the AncestryDNA team.
Once a year the math department honors students from across the state who have performed above and beyond in their math assessments. Guests will hear from professors about the opportunities that await them in college and in the workforce.
The event will take place on Wednesday, November 8, 2017 at 6:30pm in the Wilk Ballroom. If you have been invited to participate please don’t forget to rsvp at https://docs.google.com/forms/d/e/1FAIpQLSd4Xq9rA_nQRhZg7afMbJ4e7wGy0GOlNq6esoCwT-vjoOXKaA/viewform