calculus

MAA MATHFEST 2015Invited AddressesEARLE RAYMOND HEDRICK LECTURE SERIESAlgebra Over Finite FieldsKaren Smith, University of MichiganHedrick Lecture 1Wednesday, August 5, 9:30 AM – 10:20 AMMarriott Wardman Park, Salon 2/3Starting with a little trick I learned inthird grade to check my multiplicationhomework, I’ll share my fascinationwith algebra as it grew through middle school, high school,college and eventually led to research in characteristic p rings.Along the way, I’ll point out the importance of many mentorsand teachers who led me to eventually pursue my career inmathematics.Hedrick Lecture 2Friday, August 7, 9:30 AM – 10:20 AMMarriott Wardman Park, Salon 2/3In the second talk, I will explain how doing algebra over finitefields can deepen our understanding of geometry. Specifically,I’ll discuss how understanding solutions to polynomialsover finite fields can help understand the geometry ofalgebraic varieties defined by real or complex polynomials.Miraculously, rings of characteristic p have some very specialproperties that can be powerful tools in analyzing them, oftenreplacing tools like integration for real manifolds.Hedrick Lecture 3Saturday, August 8, 9:30 AM – 10:20 AMMarriott Wardman Park, Salon 2/3In the third talk, I will explain some of these recent tools in“characteristic p” algebra–specifically Frobenius splitting andrelated tools–which have made an impact on different areasof math, including the minimal model program for complexalgebraic varieties and cluster algebras in combinatorics/representation theory. Some of this work is joint work with myPhD students and post-docs.MAA100 CENTENNIAL LECTURE 1Replicators, Transformers, and Robot Swarms:Science Fiction through Geometric AlgorithmsWednesday, August 5, 8:20 AM – 9:20 AMMarriott Wardman Park, Salon 2/3Erik Demaine, MassachusettsInstitute of TechnologyScience fiction is a great inspiration forscience. How can we build reconfigurablerobots like Transformers or Terminator2? How can we build Star Trek-stylereplicators that duplicate or massproducea given shape at the nano scale?How can we orchestrate the motion ofa large swarm of robots? Recently we’ve been exploring possibleanswers to these questions through computational geometry, in thesettings of reconfigurable robots (both modular and folding robotsthat can become any possible shape), robot swarms (which may beso small and simple that they have no identity), and self-assembly(building computers and replicators out of DNA tiles).MAA100 CENTENNIAL LECTURE 2Network Science: From the Online World toCancer GenomicsWednesday, August 5, 10:30 AM – 11:20 AMMarriott Wardman Park, Salon 2/3Jennifer Chayes, Microsoft ResearchEverywhere we turn these days, we findthat networks can be used to describerelevant interactions. In the high techworld, we see the Internet, the WorldWide Web, mobile phone networks,and a variety of online social networks.In economics, we are increasinglyexperiencing both the positive andnegative effects of a global networkedeconomy. In epidemiology, we find disease spreading over our evergrowingsocial networks, complicated by mutation of the diseaseagents. In biomedical research, we are beginning to understandthe structure of gene regulatory networks, with the prospect ofusing this understanding to manage many human diseases. In thistalk, I look quite generally at some of the models we are usingto describe these networks, processes we are studying on thenetworks, algorithms we have devised for the networks, andfinally, methods we are developing to indirectly infer networkstructure from measured data. I’ll discuss in some detail particularapplications to cancer genomics, applying network algorithmsto suggest possible drug targets for certain kinds of cancer.#MAAthFestWashington, DC | August 5–8, 2015 11