About Me

I am an assistant professor in the Department of Mathematics and Statistics at the University of Massachusetts. My office is LGRT 1116, and I can be reached by email at raymond(at)math(dot)umass(dot)edu.

Here is my **CV**.

**Research interests:** I am interested in anything related to combinatorial optimization, operations research, applied algebraic geometry, proof complexity and polyhedral combinatorics.

** Outreach interests:** I am interested in thinking of different ways of making math more diverse. I run _forall on Instagram with the help of UMass student Eva Gaston. I am also invested in university-level prison education. This semester, I am teaching Math 100 at the Hampshire County Jail.

**Past** - I spent the fall semester of 2017 at the Mathematical Sciences Research Institute in Berkeley as a Gamelin Endowed Postdoctoral Fellow in the Geometric and Topological Combinatorics program. From 2014 to 2017, I was an Acting Assistant Professor (i.e., a postdoc) in the Department of Mathematics at the University of Washington working with Rekha Thomas. I completed a Ph.D. in mathematics under the supervision of Martin Grötschel at the Technische Universität Berlin. My thesis was on ''Polyhedral Methods Applied to Extremal Combinatorics Problems''. During my time in Berlin, I was also a member of the Berlin Mathematical School and of the Zuse Institute Berlin, an interdisciplinary research institute for applied mathematics and data-intensive high-performance computing. Prior to that, I was a student at the Massachusetts Institute of Technology where I completed a bachelor of science in mathematics as well as a bachelor of science (!) in music. During that time, I participated in the Undergraduate Research Opportunities Program at MIT and in two summer research programs, one funded by the NSERC and the other by the LaCIM, both in my hometown at the Université du Québec à Montréal.

**Future** - You can find me at the following seminars, conferences and workshops:

National Math Festival in Washington D.C. (May 4, 2019)

SIAM Conference on Applied Algebraic Geometry in Switzerland (July 9-13, 2019)

**Simple Graph Density Inequalities with no Sum of Squares Proofs** with Greg Blekherman, Mohit Singh and Rekha Thomas

Submitted, arXiv:1812.08820

**The Bullet Problem with Discrete Speeds** with Brittany Dygert*, Matthew Junge, Christoph Kinzel*, Erik Slivken and Jennifer Zhu*

Submitted, arXiv:1610.00282 (* denotes undergrad coauthors)

**The Turán Polytope**

The Electronic Journal of Combinatorics, Volume 25, Issue 3 (2018), P3.43

**Symmetric Sums of Squares over k-Subset Hypercubes** with James Saunderson, Mohit Singh and Rekha Thomas

Mathematical Programming Series A, Volume 167, Issue 2 (2018), pp. 315-354

**Symmetry in Turan Sums of Squares Polynomials from Flag Algebras** with Mohit Singh and Rekha Thomas

Algebraic Combinatorics, Volume 1, Number 2 (2018), pp. 249-274.

**New Conjectures for Union-Closed Families** with Jonad Pulaj and Dirk Theis

The Electronic Journal of Combinatorics, Volume 23, Issue 3 (2016), P23.3

**Standings in Sports Competitions Using Integer Programming** with Christian Raack, Thomas Schlechte and Axel Werner

Journal of Quantitative Analysis in Sports, Volume 10, Issue 2 (2014), pp. 131-138

**Multiband Robust Optimization and its Adoption in Harvest Scheduling** with Fabio D'Andreagiovanni

FORMATH, Forest Resource Management and Mathematical Modeling International Symposium, Volume 13 (2013)

**0-1 Multiband Robust Optimization** with Christina Büsing and Fabio D'Andreagiovanni

Operations Research Proceedings 2013, pp. 89-96

**Robust Optimization under Multiband Uncertainty** with Christina Büsing and Fabio D'Andreagiovanni

Proceedings of the Workshop on Mixed Integer Programming 2013

**The Centers of Gravity of the Associahedron and of the Permutahedron Are the Same** with Christophe Hohlweg and Jonathan Lortie

The Electronic Journal of Combinatorics, Volume 17, Issue 1 (2010), R72

**Small Chvátal Rank** with Tristram Bogart and Rekha Thomas

Mathematical Programming, Volume 124, Issue 1-2 (2010), pp 45-68

**Spring Semester 2019: Math 100 Math for the Real World**: 5 students

**Fall Semeseter 2019: Biweekly Math Circle**: 15 students.

**Spring Semester 2019: Math 697 Combinatorial Optimization **: 18 students.

**Fall Semester 2018: Math 455 Discrete Mathematics**: 25 students.

**Spring Semester 2018: Math 455 Discrete Mathematics**: 27 students.

**Fall Semester 2017: Elementary Algebra** 28 students, co-taught with Dan Walls and Tomas Leon. This class was taught through the Prison University Project, an organization whose mission is to provide excellent higher education to people at San Quentin State Prison; to support increased access to higher education for incarcerated people; and to stimulate public awareness about higher education access and criminal justice. This course was meant to teach students the foundational tools needed for higher mathematics and a language for understanding the principles of science, engineering, economics, etc.

**Spring Semester 2017: MATH 106 College Algebra** 11 students + 3 auditors. This class is taught through University Beyond Bars, an organization providing higher education to people in prisons. The students earn credits for this course through Adams State University. This course is meant to be an introduction to the basic techniques of algebra. Topics include functions, systems of equations, matrix algebra, inequalities, and complex numbers. Weekly homework, four midterms, one final, two hands-on projects where the students applied what they learned to their daily lives.

**Fall Semester 2016: Lecture Series on Proofs from the Book** This lecture series was organized through University Beyond Bars. It provided an introduction to the world of mathematical proofs.

**Spring Semester 2016: MATH 104 Finite Mathematics** 16 students + 4 auditors. This class was taught through University Beyond Bars, and students earned credits through Adams State University. This course covered some introductory topics in combinatorics, probability, statistics, linear algebra and optimization. Weekly homework and quizzes, one midterm, one final, two hands-on projects where the students applied what they learned to their daily lives.

**Spring Quarter 2017: MATH 300 Introduction to Mathematical Reasoning** 32 students. An introduction to mathematical arguments and the writing of proofs through topics in elementary set theory, graph theory and number theory. Weekly homework and quizzes every other week, one midterm, one final.

**Spring Quarter 2017: MATH 324 Advanced Multivariable Calculus** 50 students. As below.

**Winter Quarter 2016: MATH 498A Special Topics in Mathematics ** 1 student. Reading course with an undergrad student on approximation algorithms.

**Fall Quarter 2016: MATH 324 Advanced Multivariable Calculus** 100 students over two sections. As below.

** Spring Quarter 2016: MATH 409 Combinatorial Optimization** 27 students. This course covered various topics connected to matchings and matroids from a polyhedral perspective. Weekly homework and quizzes, one midterm, one final.

**Spring Quarter 2016: MATH 498 Special Topics in Mathematics ** 1 student. Research with an undergrad student on the union-closed sets conjecture.

**Winter Quarter 2016: MATH 324 Advanced Multivariable Calculus** 92 students over two sections. As below with the addition of ASK or Annie's Survival Kit, three extra problems with carefully written out solutions sent weekly to better prepare the students for the quizzes. An extra ASK office hour right before the quiz was also added where I went over the problems and showed my thought process.

**Fall Quarter 2015: MATH 324 Advanced Multivariable Calculus ** 88 students over two sections. As below with the removal of one midterm and the addition of two extra-credit projects. The first one asked students to find out about an application of multivariable calculus relevant for their future career or their interests. The second one asked them to use Lagrange multipliers to optimize something in their lives.

**Spring Quarter 2015: MATH 308 Matrix Algebra With Applications** 49 students. As below with the addition of an extra-credit project where the students had to think about an advanced application of linear algebra (i.e., not just solving) relevant for their future career or their interests.

**Winter Quarter 2015: MATH 308 Matrix Algebra With Applications** 46 students. This is an introduction to linear algebra which covered solving systems of linear equations, matrix algebra, vector spaces, orthogonality, least squares, eigenvalues, diagonalization. Weekly homework through WebAssign as well as weekly quizzes, one midterm and one final.

**Fall Quarter 2014: MATH 324 Advanced Multivariable Calculus** 94 students over two sections. This course covered double and triple integrals in different coordinate systems, as well as line and surface integrals to culminate with Stokes' theorem and the Divergence Theorem. Weekly homework through WebAssign as well as weekly quizzes, two midterms and one final.

**Winter Semester 2011-2012: Proof Techniques in Polyhedral Combinatorics ** 10 students. Seminar for advanced undergrad students and master students co-taught with Martin Grötschel. Lectured the first few weeks and then helped the students to choose a topic of their own to study and then advised them in their research.