Ilia Itenberg, University of Strasbourg and MSRI Thursday, September 3 2:30pm Tropical geometry ABSTRACT The purpose of the talk is to make an introduction to tropical geometry, a new mathematical domain which has undergone a spectacular progress during the last nine years. In tropical geometry, algebro-geometric objects are replaced with piecewise-linear ones. For example, the tropical curves in the plane are certain rectilinear graphs. We will present the basic tropical notions and the first results in tropical geometry limiting ourselves to planar tropical curves.
 Kirsten Eisentraeger, Penn State Thursday, September 17 2:30pm Using elliptic and hyperelliptic curves in pairing-based cryptography ABSTRACT Over the past years, many new and exciting cryptographic schemes based on pairings have been suggested, including one-round three-way key establishment, identity-based encryption, and short signatures. Originally, the Weil and Tate pairings on supersingular elliptic curves were proposed for such applications, providing non-degenerate bilinear maps that are efficient to evaluate. As an alternative to elliptic curve groups, Koblitz suggested hyperelliptic curves for use in cryptography. In this talk we will explain how elliptic and hyperelliptic curves are used in these applications, and we will explain some of the techniques to optimize computations of elliptic and hyperelliptic pairings.
 Matthias Weber, Indiana University Thursday, September 24 2:30pm An Invitation to Minimal Surfaces ABSTRACT Minimal Surfaces have attracted mathematicians for over 300 years. While much progress has been made, the key question remains: What are the possible topological types of complete, embedded minimal surfaces. This talk will be very elementary with many pictures.
 Mark Levi, Penn State Thursday, October 1 2:30pm Discovering and proving theorems by physical reasoning ABSTRACT Physics often provides mathematics not only with a problem, but also with the idea of a solution. Some calculus problems can be solved more quickly without calculus, by using physics instead. A few examples of such problems will be given in a part of this talk. In addition to these problems, quite a few theorems which may seem somewhat mysterious become completely obvious when given a proper physical incarnation. This is the case for both elementary" theorems (the Pythagorean theorem, Pappus' theorems, some trig identities, and many, many more) and the less elementary ones: Noether's theorem, the preservation of Poincare's integral invariants, the Gauss-Bonnet theorem, the Riemann Mapping Theorem, Green's theorem, Moser's theorem on uniformization of density, etc. (no familiarity with any of these is assumed). I will describe a miscellaneous sampling from the above list, according to the audience's interest. No background beyond calculus and basic mechanics will be assumed in this talk.
 Luca Capogna, University of Arkansas Thursday, October 22 2:30pm Minimal surfaces in sub-Riemannian geometry
 Jon Chaika, N/A Thursday, October 29 2:30pm [0,1] is not a minimality detector of [0,1]^2 ABSTRACT This talk will introduce the notion of minimal sequences. It will then show that [0,1]^2 can detect the minimality of sequences in any compact metric space. However, [0,1] can not detect the minimality of sequences in [0,1]^2.
 Svetlana Katok, Penn State Thursday, November 5 2:30pm Everything you wanted to know about 2x2 matrices ABSTRACT The group SL(2,R) is at the junction of number theory, representation theory, topology, geometry and dynamics. This seemingly simple object is both a source of deep questions and a proving ground for a variety of methods. We will reveal some surprising connections between arithmetic, geometry and dynamics that arise from the study of this interesting group.
 Robert Ghrist, University of Pennsylvania Thursday, November 12 2:30pm Topological Network Topology ABSTRACT Networks are ubiquitous: communications networks, social networks, sensor networks, biological networks, etc., abound. "Network topology" is, usually, a misnomer, connoting graph theory. This talk will, via simple examples, argue for a topological interpretation of networks that, via algebraic topology, reveals classes of information hidden within networks around us.
 S. Weinberger, University of Chocago Thursday, December 3 2:30pm Topology and Social Choice ABSTRACT Often one is in the situation when there are many agents or voters who each have an idea of what should be done, and we must find some way to combine their preferences and decide what "society wants". (This might even be what happens in an individual, where various subroutines in the brain each calculate a preference based on the function they are designed to "want" to optimize.) It turns out that this is rarely possible, but that one can have a lot of geometric and topological fun thinking about and manipulating such elections.
 Anton Petrunin, Penn State Thursday, October 8 2:30pm Two problems in combinatorial plane geometry ABSTRACT It is a story, how I was making exercises for school students and what happened after it.
 Frederick Cohen, University of Rochester Thursday, October 15 2:30pm Braid groups and their applications ABSTRACT Braids are easy to picture. The purpose of this talk is to describe Borromean braids as well as what these 'measure'.