Steven Simon

Assistant Professor of Mathematics

Biography

I have been at Bard since Fall 2016, first as a visiting and as of Fall 2018 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 as a MacCracken Fellow under Sylvain Cappell 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 2019, I am teaching MATH 312 (Advanced Calculus) and MATH 105 (Time, Space, and Infinity: Mathematical Perspectives on Philosophical Paradoxes), the later being a course I designed on Zeno's paradoxes and the mathematics (irrational numbers, infinite series, and cardinality) used in "resolving" them. All of my 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 321 (Differential Equations) Sp 2019

MATH 312 (Advanced Calculus) F 2019

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 and 2019, Sp 2018-2019, cross-listed with Philosophy and Experimental Humanities.

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 their use in answering questions in as well as motivated by those from 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), 3759--3768. DOI: 10.2298/FIL1811759S

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

Research with Undergraduates

[7] Regular Polygonal Tverberg-Type Theorems (with L. Leiner), in preparation.

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

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)