Steven Simon

Assistant Professor of Mathematics

Biography

I have been at Bard since Fall 2016, first as a visiting and now as a tenure-track Assistant Professor in the Mathematics Program. Before that, I was a Visiting Lecturer at Wellesley College (Fall 2013-Spring 2016) and a Visiting Assistant Professor at the Cooper Union for the Advancement of Science and Art (Fall 2011-Spring 2013) in the Albert Nerken School of Engineering. In Summers 2013 and 2014, I was a Visiting Postdoctoral Researcher at the Hebrew University of Jerusalem under the supervision of Gil Kalai. I received my Ph.D. from the Courant Institute of Mathematical Sciences (New York University) in 2011 under Sylvain Cappell as a MacCracken Fellow, and my B.A. in mathematics from Yale University in 2005 after switching from a major in Philosophy at the beginning of my junior year.

Teaching

In Fall 2018, I am teaching MATH 361 (Real Analysis), MATH 328 (Probability), and MATH 261 (Proofs and Fundamentals). All course materials are available on Moodle. My past and current teaching is listed below:

Bard College

MATH 361 (Real Analysis) F 2017-2018 and Sp 2016

MATH 332 (Abstract Algebra) F 2016

MATH 328 (Probability) F 2018

MATH 261 (Proofs and Fundamentals) F 2018

MATH 245 (Intermediate Calculus) Sp 2018

MATH 142 (Calculus II) F 2016-Sp 2017

MATH 105 (Time, Space, and Infinity: Mathematical Perspectives on Philosophical Paradoxes) F 2017-Sp 2018

Wellesley College

MATH 205 (Multivariable Calculus) F 2015-Sp 2016

MATH 116 (Calculus II) F 2013 and 2015

MATH 115 (Calculus I) F 2013-2014 and Sp 2014-2016

Cooper Union

MATH 240 (Ordinary and Partial Differential Equations) F 2011-Sp 2013

MATH 223 (Vector Calculus) F 2011-Sp 2013

Research

My research is centered on applications of algebraic and geometric topology, with special emphasis on using their methodologies to answer questions in geometric combinatorics and discrete geometry. I am especially interested in mass equipartitions (fair division problems for continuous and discrete measures, generalizing the classical "Ham Sandwich" theorem), as well as generalizations of Tverberg's theorem from convex geometry.

Publications

[1] G-ham sandwich theorems: balancing measures by finite subgroups of spheres, Journal of Combinatorial Theory, Series A 120 (2013) 1906--1912. DOI:10.1016/j.jcta.2013.07.007

[2] Measure equipartitions via finite Fourier analysis, Geometriae Dedicata 179 (2015) 217--228. DOI:10.1007/s10711-015-0077-5

[3] Average-value Tverberg partitions via finite Fourier analysis, Israel Journal of Mathematics 216 (2016) 891--904. DOI: 10.1007/s11856-016-1432-4

[4] Measure partitions via Fourier analysis II: center transversality in the L^2-norm for complex hyperplanes, Journal of Geometry 107 (2016) 593--601. DOI:10.1007/s00022-015-0291-1

[5] Mass partitions via equivariant sections of Stiefel bundles, Filomat 32 (2018).

[6] Hyperplane equipartitions plus constraints, Journal of Combinatorial Theory, Series A 161 (2019) 29--50. DOI:10.1016/j.jcta.2018.07.012

In Preparation

[7] Hyperplane equipartitions plus constraints II: Makeev-type problems (with A. Meja and J. Zhang).

[8] Affine and topological Tverberg-type theorems with regular polyhedral symmetry (with L. Leiner).


Recent Conferences

1. Institute for Computational and Experimental Research in Mathematics (ICERM). Topology and Geometry in a Discrete Setting, Invited Speaker (Nov 28-Dec 2, 2016)

2. SIAM Conference on Applied Algebraic Geometry. Minisymposium on Symmetric Simplicial Complexes and Polytopes, Invited Speaker (Jul 31-Aug 4, 2017)

3. Institute of Mathematics Polish Academy of Sciences (IMPAL). Applied Topology in Będlewo, Contributing Speaker (Jun 25-Jul 1, 2017)

4. Mathematical Science Research Institute (MSRI). Geometric and Topological Combinatorics: Modern Techniques and Methods, Travel Award (Oct 9-13, 2017)

5. American Mathematical Society (AMS) Spring Eastern Sectional Meeting. Special Session on Algebraic, Geometric, and Topological Methods in Combinatorics, Invited Speaker (Apr 21-22, 2018)