Matthew J. Samuel

I am a 4^th year graduate student in the mathematics PhD program at Rutgers University, New Brunswick.

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Contact Information

Office: Hill 620

Office hours: Wednesday 1:40-3:00

E-mail: msamuel at math dot rutgers dot edu

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Teaching

Fall 2011, 135: Calculus I

Summer 2011, 477: Mathematical Theory of Probability

Spring 2011, 115: Precalculus College Mathematics

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Research

I woke up one morning and found that I had somehow become entangled in researching algebraic combinatorics. My advisor is Anders Buch.

Papers

· Equivariant Schubert Calculus on Isotropic Grassmannians, Henry Rutgers Scholars thesis, Rutgers University, April 2008. (Here's a list of the Henry Rutgers Scholars who graduated in 2008.)

· Word posets, complexity, and Coxeter groups, arXiv:1101.4655v1 [math.CO]

· Abstract root systems and intervals in weak Bruhat order (extended abstract), Electronic Notes in Discrete Mathematics 38 (2011), pp. 481-486.

· A new analog of permutation patterns for general Coxeter groups, submitted.

· Abstract root systems and weak order intervals, submitted.

· The number of weak order intervals, in preparation.

· K-theory of minuscule varieties (with Anders Buch), in preparation.

Talks

· Reduced words, linear extensions, and permutations, CombinaTexas, Southwestern University, April 21^st, 2012

· Two formulas for the equivariant cohomology of complete flag varieties, Binghamton University Graduate Conference in Algebra and Topology, November 12^th, 2011.

· Word posets, with applications to Coxeter groups, International Conference on Words, Czech Technical University/Charles University, September 16^th, 2011.

· Abstract root systems and intervals in weak Bruhat order, European Conference on Combinatorics, Graph Theory and Applications, Alfréd Rényi Institute of Mathematics, August 30^th, 2011 (CANCELLED DUE TO WEATHER)

· The number of weak order intervals, British Combinatorial Conference, University of Exeter, July 6^th, 2011.

· Permutation patterns in Coxeter groups, Permutation Patterns, California Polytechnic State University, June 22^nd, 2011.

· Counting in Coxeter groups, CombinaTexas, Sam Houston State University, April 16^th, 2011.

· Words in Coxeter groups, Binghamton University Graduate Conference in Algebra and Topology, Binghamton University, November 6^th, 2010.

· Combinatorics of Grassmannians, Graduate Student Topology and Geometry Conference, University of Michigan—Ann Arbor, April 11^th, 2010.

· Equivariant Cohomology of Isotropic Grassmannians, Binghamton University Graduate Conference in Algebra and Topology, Binghamton University, November 14^th, 2009.

· Equivariant Schubert Calculus on Isotropic Grassmannians, Garden State Undergraduate Mathematics Conference, William Paterson University, April 12^th, 2008.

· Towards a Positive Rule for the Equivariant Cohomology of Lagrangian Grassmannians (with Charles Siegel), Young Mathematician's Conference, Ohio State University, August 18^th, 2007.

Poster(s)

· Equivariant Schubert Calculus on Grassmannians of Types B and C, Aresty Undergraduate Research Symposium, Rutgers University, April 25^th, 2008.

Other

· Number of commutation classes of reduced words for the longest element of a Weyl group of type B_n, sequence A180605 in the Online Encyclopedia of Integer Sequences.

· Number of commutation classes of reduced words for the longest element of a Weyl group of type D_n, sequence A180607 in the Online Encyclopedia of Integer Sequences.

· Number of isomorphism classes of partially ordered sets of length n that occur as intervals in weak Bruhat order of some Coxeter group, sequence A185349 in the Online Encyclopedia of Integer Sequences.

· Number of isomorphism classes of Coxeter systems with n reflections, sequence A19105 in the Online Encyclopedia of Integer Sequences.

· Enumeration of small weak order intervals.

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In Memory of my Father, Richard Irving Samuel

Dick Samuel died on March 20^th, 2011 from complications of adult respiratory distress syndrome. He was 71 years old. His obituary can be found here. Among other things, he was an accomplished patent attorney. His work for Gordon Gould, the inventor of the laser, is immortalized in the book Laser: The Inventor, the Nobel Laureate, and the Thirty-Year Patent War by Nick Taylor. He was able to secure dozens of patents for Gould and worked tirelessly to ensure that Gould was paid the royalties he was due. Wikipedia calls it “one of the most important patent battles in history.” A short summary can be found in the article Patent Pending published in 1989.

This was by no means my father’s only achievement. Whenever he set his mind to something, he didn’t rest until he succeeded. Even though he was always busy with something, he was always there for his family. We all loved him, and we will always miss him.