RUTGERS EXPERIMENTAL MATHEMATICS SEMINAR

sponsored by the

Rutgers University
Department of Mathematics

and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

Founded 2003 by Drew Sills and Doron Zeilberger.

Former co-organizers: Drew Sills (2003-2007), Moa ApaGodu (2005-2006), Lara Pudwell (2006-2008), Andrew Baxter (2008-2011), Brian Nakamura (2011-2013), Edinah Gnang (2011-2013), Matthew Russell (2013-2016)

Current co-organizers:
Doron Zeilberger (doronzeil {at} gmail [dot] com)
Nathan Fox (fox {at} math [dot] rutgers [dot] edu)

Archive of Previous Speakers and Talks You can find links to videos of some of these talks as well. Currently, our videos are being posted to our Vimeo page. Previously, we had videos posted on our YouTube page.


If you would like to be added to the weekly mailing list, email Nathan Fox (fox@math...).

Forthcoming Talks

Unless otherwise specified, seminars will be held in Hill 705 on the date indicated from 5:00 to 5:48 PM. Professor Zeilberger has promised to enforce the time limits.




Spring 2017

Date: March 23, 2017
Speaker: Justin Semonsen, Rutgers University
Title: On Oda's Strong Factorization Conjecture
Abstract:
          In this talk we will translate a conjecture by Oda about birational maps of toric varieties into a conjecture about fans of simplicial cones. Further combinatorial techniques reduce the conjecture to an algorithmic form suitable for computation and experimentation. Experimental results gotten via Java provide insight into how one might prove the conjecture via a much simpler mechanism.


Date: March 30, 2017
Speaker: Nathan Fox, Rutgers University
Title: An Exploration of Nested Recurrences Using Experimental Mathematics (thesis defense)
Abstract:
          Nested recurrence relations, such as the Hofstadter Q-recurrence Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)), have no general theory. Solutions are highly dependent on the initial conditions, and many sequences they generate are not even known to be infinite. In this talk, we will see a variety of results pertaining to sequences arising from nested recurrences. These results include a method of automatically discovering solutions of a particular form, some sequences exhibiting never-before-seen behavior, and methodology for analyzing entire families of initial conditions simultaneously.


Date: April 6, 2017 (rescheduled from February 9, 2017)
Speaker: Evita Nestoridi, Princeton University
Title: Shuffling large decks of cards and the Bernoulli-Laplace urn model
Abstract:
          In board games, in Casino games with multiple decks and cryptography, one is sometimes faced with the practical problem: how can a human (as opposed to the computer) shuffle big decks of cards. One natural procedure (used by casinos) is to break the deck into several reasonable size piles, shuffle each thoroughly, assemble, do some simple deterministic thing (like a cut) and repeat. G. White and I introduce variations of the classical Bernoulli-Laplace urn model (the first Markov chain!) involving swaps of big groups of balls. A coupling argument and spherical function theory allow the original problem to be solved.


Date: April 13, 2017
Speaker: Aaron Robertson, Colgate University
Title: TBA


Date: April 20, 2017
Speaker: Joe Kileel, Univ. of California, Berkeley
Title: Using Computational Algebra for Computer Vision
Abstract:
          Scene reconstruction is a fundamental task in computer vision: given multiple images from different angles, create a 3D model of a world scene. Nowadays self-driving cars need to do 3D reconstruction in real-time, to navigate their surroundings. In this talk, we will explain how key subroutines in reconstruction algorithms amount to solving polynomial systems. We will quantify the "algebraic complexity" of systems that engineers have been hoping to solve quickly and reliably for some while. Our approach combines symbolic and numerical methods from computational algebra. Those wondering "if algebraic geometry is good for anything practical" are especially encouraged to attend.


Date: April 27, 2017
Speaker: Vince Vatter, University of Florida
Title: TBA





This page is maintained by Nathan Fox. Send comments to fox {at} math [dot] rutgers [dot] edu.