Steven Simon

Bard College

I have been a Visiting Assistant Professor at Bard since Fall 2016, with prior appointments as a Visiting Lecturer at Wellesley College (Fall 2013-Spring 2016) and as 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. 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

This semester, I am teaching MATH 361 (Real Analysis) and MATH 105 (Time, Space, Infinity: Mathematical Perspectives on Philosophical Paradoxes), a new non-majors course cross-listed with philosophy which I have been designing over the course of the past year. All materials from my courses are on Moodle. My past and current teaching is listed below:

Bard College

MATH 361 (Real Analysis), Spring 2016-Fall 2017

MATH 332 (Abstract Algebra), Fall 2016

MATH 142 (Calculus II), Fall 2016-Spring 2017

MATH 105 (Time, Space, Infinity: Mathematical Perspectives on Philosophical Paradoxes), Fall 2017

Wellesley College

MATH 205 (Multivariable Calculus), Fall 2015-Spring 2016

MATH 116 (Calculus II), Fall 2013 and 2015

MATH 115 (Calculus I), Fall 2013-2014 and Spring 2014-2016

Cooper Union

MATH 240 (Ordinary and Partial Differential Equations), Fall 2011-Spring 2013

MATH 223 (Vector Calculus), Fall 2011-Spring 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] Hyperplane equipartitions plus constraints, arXiv:1708.00527 [math.MG] (2017). Submitted

[6] Mass partitions via equivariant sections of Stiefel bundles, arXiv:1011.1922 [math.CO].

[7] Optimal bounds for constrained Makeev-type problems. In preparation

Recent and Upcoming 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)