Colloquium SeriesSpring 2013Unless otherwise noted, talks will be at 3:50 PM in Alumni Science 120. Also, there will be refreshments before each talk in O'Connor 31 at 3:30 PM. Tuesday, April 15th Speaker: Natalie Linnell and Silvia Figueira, Santa Clara UniversityTitle: Technology for Good: Frugal Innovation and Apps for the Homeless Abstract: Technology has transformed the way the average American lives, and there’s no reason that technology can’t also have a positive impact on the lives of underserved populations around the globe. In this talk, we’ll discuss the work of the Frugal Innovation lab here at Santa Clara University, which engages Santa Clara students in creating new technologies to serve these populations. In addition to giving an overview of the lab’s recent activities, we will discuss indepth the Streetconnect project. Streetconnect is a textmessage broadcast service designed to connect the homeless of our local area with NGOs (nongovernmental organizations) who provide services to them. This is a nontechnical talk, accessible to all (especially students!)
Tuesday, April 22nd Speaker: Viktor Ginzburg, University of California at Santa CruzTitle: Periodic Orbits of Hamiltonian Systems Abstract: Since the time of Newton, periodic orbits have played a central role in the study of dynamical systems. In general, Hamiltonian systems meeting certain simple natural requirements tend to have an abundance of periodic orbits. However, proving their existence is often a highly nontrivial task leading to new insights (e.g., the Arnold conjecture and the Weinstein conjecture) and requiring new methods (e.g., the Floer homology) of interest and importance to many areas of mathematics. In this nontechnical talk we will focus on the existence problem for periodic orbits in the context of symplectic geometry and discuss some of the recent results and conjectures.
Tuesday, April 29th Title: Normal polytopes Abstract: Examples of polytopes are polygons, Platonic solids, more general shapes and their higher dimensional analogs. A polytope is called lattice if its vertices have integer coordinates, and a lattice polytope is called normal if it satisfies a very natural and simple arithmetic condition, making the discrete set of integer points in the polytope a correct analogue of a continuous polytope. Many conjectures have been proposed on succinct geometric characterizations of the normality property  all of them disproved in the late 1990s and early 2000s. Normal polytopes are building blocks for toric varieties, but we will not talk on toric algebraic geometry. In the talk we will survey the previous work on counterexamples by Aguzzoli, Bouvier, Bruns, GonzalezSprinberg, Henk, Martin, Mundici, Weismantel, and the speaker. Then, time permitting, we will describe new challenges in normal polytopes, inspired by a new topological approach, partly implicit in the previous work and a subject of considerable interest in itself. The talk assumes no background, except some familiarity with linear algebra, and it should be understandable to advanced undergraduates. Tuesday, May 6th Speaker: Eric Madia (’95), FCAS, MAAA  Esurance Title: Auto Insurance Premiums – The Science Behind the Mystery*** A Pi Mu Epsilon Sponsored Event Abstract: We all fork over large amounts of money each year for a product that we can't see or touch. Moreover, we get no value (besides financial security and the right to be lawful) from such a product unless we are the unfortunate 10% of the population involved in an auto accident in a given year. So why does auto insurance cost so much and why do 2 seemingly similar people pay vastly different amounts? In this talk we'll explore at a high level how auto insurance premium is determined and some of the math behind it. More importantly, we'll discuss the value that casualty actuaries add to the process and why it is a profession in high demand and consistently regarded as a top 5 career choice. For those of you looking at the actuarial profession as a potential career, we will set aside time to also discuss what you can do now to prepare yourself, what to emphasize on your resume, and any other questions that you may have about the Casualty Actuarial Society and the profession. Tuesday, May 13th Speaker: Rick Schulte, Santa Clara UniversityTitle: Building a Better Bracket: A Statistical Model for the NCAA Tournament Abstract: Each year, tens of millions of Americans participate in contests or betting pools related to the NCAA men’s basketball tournament, or “March Madness.” For the savvy prognosticator, there is potentially a lot of money up for grabs – for evidence, one has look no farther than this year’s “Billion Dollar Bracket Challenge,” bankrolled by Warren Buffet. I will present a simple model that uses a combination of human and computer ranking systems to predict the outcome of both single games and entire tournaments. By several evaluation metrics, the model’s performance is superior to seedonly models as well as pundit predictions. I will also outline a strategy by which to maximize one’s expect return in a bracket pool using a Markov chain Monte Carlo algorithm. Tuesday, May 27th Speaker: Nayantara Bhatnagar, University of Delaware Title: Lengths of Monotone Subsequences in Random Mallows Permutations Abstract: The longest increasing subsequence of a uniformly random permutation (LIS) is a well studied problem. Vershik Kerov and LoganShepp first showed that asymptotically the typical length of the LIS is 2sqrt(n) using connections to Young tableaux. This line of research culminated in the work of BaikDeiftJohansson who related this length to the TracyWidom distribution. We study the lengths of the longest increasing and decreasing subsequences of random permutations drawn from the Mallows measure, introduced by Mallows in connection with ranking problems in statistics. This is joint work with Ron Peled.
Relevant background for the talk will be introduced as needed. Tuesday, June 3rd Speaker: Eric Hsu, San Francisco State University Title: Teaching Calculus: Group Work, Flips and Department Culture Abstract: We will discuss research on teaching calculus along with personal experiences, touching on techniques such as group work and flipped classrooms. We will discuss the Emerging Scholars Program model for promoting the success of underrepresented minorities. We will also discuss some early results from a large national study of college calculus instruction by the MAA on student retention and the department structures that nurture effective teaching.  WINTER QUARTER 2014  Tuesday, January 21st
Speaker: Slobodan Simić, San Jose State University Title: A dictionary of chaos Abstract: The term "chaos" has been part of popular culture at least since Spielberg’s Jurassic Park, but in the field of mathematics called dynamical systems, chaos has been studied for over a century. In this expository talk aimed at beginning graduate and advanced undergraduate students, I will describe a basic "dictionary" of chaos, mostly through examples, and give an overall feel for what current research in dynamical systems is like. Tuesday, February 4th Speaker: Anthony Bak, Ayasdi Title: Topological Data Analysis and Big Data Abstract: I will discuss how Ayasdi uses Topological Data Analysis to solve complex problems. We'll start with an overview of TDA and describe the core algorithm, "Mapper". We'll end with a demonstration of how we how this is used to solve real world problems. The talk should be understandable by mathematics and computer science undergraduates.
Speaker: Ellen Veomett, Saint Mary's College Title: Coloring Geometrically Defined Graphs
Abstract: This talk will take us through a journey of graph coloring. We'll start with some basic definitions and the wellknown four and five color theorems. We'll also discuss the fascinating question of the chromatic number of the plane. Finally, we'll talk about new results on box graphs, which are graphs defined using blocks and their intersections. This talk will be extremely accessible, while at the same time including some modern research topics. Tuesday, March 4th
Speaker: Sara Malec, University of the Pacific
Title: On the Intersection Algebra of Ideals
Abstract:The intersection algebra of two ideals in a ring is an object that encodes information about the intersections of powers of both ideals. These algebras have many interesting properties, and in certain cases they are finitely generated. The proof of this fact relies heavily on semigroup theory, specifically semigroups coming from pointed rational cones. In my talk, I will introduce the necessary concepts from the theory of semigroups, and use them to present several important facts about these algebras.
Tuesday, March 11th
Speaker: Sayanti Banerjee, Santa Clara University
Title: The Dynamics of Puberty *** A Pi Mu Epsilon Sponsored Event
Abstract: We all experience puberty, yet biologically it remains very puzzling: no one knows how puberty gets started. Identifying the mechanisms underlying the onset of puberty is a critical issue given the earlier onset of puberty in girls and boys in the past century, a change that has broad implications on the health and wellbeing of young men and women. A big part of the answer is a change in activity of a particular group of neurons (nerve cells). I will discuss what is known about the biological basis of puberty and describe how mathematical models can help us gain insights into possible mechanisms of puberty. If you have a disability and require a reasonable accommodation, 
Abstracts of previous talks are available here.
