Professor Sinai Robins, PhD
sinai.robins@gmail.comCitizenship: USANative language: EnglishEducation
1991, PhD in Mathematics, University of California, Los Angeles (UCLA).
1987, MS in Mathematics, University of California, Los Angeles (UCLA).
1986, BA in Mathematics, with highest honors, University of California, Los Angeles (UCLA).
Research Interests
My research interests include discrete and computational geometry, Fourier and harmonic analysis, number theory, combinatorics, and combinatorial optimization, with a focus on lattice-point enumeration, Ehrhart theory, and tilings, as well as Fourier methods in machine learning and neural networks. I am also interested in applying rigorous mathematics to AI, particularly mathematical reasoning, automated discovery, and the evaluation of AI systems on research-level problems.
Books
M. Beck and S. Robins, Computing the continuous discretely: integer-point enumeration in polyhedra, Springer Undergraduate Texts in Mathematics, 2nd edition, 2015. Translated by Springer into German and Japanese editions.
S. Robins, Fourier analysis on polytopes, and the geometry of numbers, part I: a friendly introduction, American Mathematical Society, Student Mathematical Library, Volume 107, 2024: https://bookstore.ams.org/view?ProductCode=STML/107
A preliminary version is available on arXiv: https://arxiv.org/abs/2104.06407
Academic Career
2016–present, Full Professor of Mathematics, University of São Paulo (IME-USP), Brazil.
2015–2017, Deputy Director, ICERM (Institute for Computational and Experimental Research in Mathematics), Brown University.
2014–2015, Distinguished Visiting Professor of Mathematics, Brown University.
2013 (April–December), Research Visitor, CNRS/LAAS, Toulouse, France.
2011 (March–June), Research Visitor, Alfréd Rényi Institute of Mathematics, Budapest, Hungary.
2008–2014, Tenured Associate Professor, Nanyang Technological University, Singapore.
2008, Adjunct Professor, University of Newcastle, Australia.
2000–2007, Tenured Associate Professor, Temple University.
2000–2001, Research Visitor (sabbatical), Technion – Israel Institute of Technology, Department of Industrial Engineering; research and teaching in combinatorial optimization and operations research.
1998 and 2000, Research Consultant, Communications Research, Institute for Defense Analyses (IDA), La Jolla.
1997–2000, Assistant Professor, Temple University.
1996–1997, Postdoctoral Fellow, Mathematical Sciences Research Institute (MSRI), Berkeley.
1995–1998, National Science Foundation (NSF) Postdoctoral Fellow and Visiting Professor, UC San Diego.
1991–1995, University of Northern Colorado; tenured and promoted to Associate Professor in 1995.
1986–1991, Sloan Fellow (dissertation award from the Sloan Foundation).
1986–1990, UCLA Chancellor's Fellow (the highest fellowship awarded to UCLA graduate students).
1985–1986, Electrical Engineer, Hughes Aircraft, El Segundo, Electro-Optical and Data Systems Group; research in infrared optical recognition.
Publications
Complete publication list on the Research page.
Undergraduate Publications and informal articles
S. Robins, "The Rotating Coin Puzzle," UCLA Undergraduate Science Journal, 1986.
S. Robins, "The Zen of Mathematics," The Mirror (University of Northern Colorado newspaper), December 1991.
Editorial Work
Founding and Managing Editor, Online Journal of Analytic Combinatorics (OJAC), 2005–present, co-founded with Alex Iosevich and Izabella Łaba. The journal is freely available at math.rochester.edu/ojac.
Editor, The Ramanujan Journal, 2012–2024.
Editor, Journal of Fourier Analysis and Applications, 2025–present.
Grants and Awards
2024, Teaching Award, School of Business, University of São Paulo.
2018–2019, CNPq research grant (National Council for Scientific and Technological Development, Brazil).
2014–2015, Distinguished Visiting Professor of Mathematics, Brown University.
2012–2015, Tier-2 research grant, Singapore Ministry of Education, co-PI (US$586,000).
2013–2014 (November–January), Institute for Mathematical Sciences (IMS) joint grant to run a three-month program on inverse moment problems, Singapore (US$130,000).
2012 (October), London Mathematical Society visiting researcher grant to UCL, Oxford, and Cambridge.
2010 and 2005, Clifford Lecturer, Tulane University.
2008–2011, Start-Up Grant, Nanyang Technological University, Singapore (US$45,000).
2007, American Institute of Mathematics (AIM) funded week-long workshop on convexity and Fourier analysis, Palo Alto, California.
2005, MSRI/BIRS award to teach a summer course with Matthias Beck, Banff, Canada.
2000–2003, NSA Young Investigator Award (US$91,500).
1998, Summer Research Stipend, Temple University (US$4,500).
1996, Postdoctoral Fellowship, Mathematical Sciences Research Institute (US$22,000).
1995, National Science Foundation (NSF) Postdoctoral Fellowship (US$75,000).
1995, National Science Foundation (NSF) research grant (US$105,000).
1990, Sloan Foundation Dissertation Fellowship (US$14,700).
1986, UCLA Chancellor's Fellowship, the highest fellowship awarded to a UCLA graduate student.
1986, Phi Beta Kappa, UCLA.
1986, UCLA Sherwood Prize in Mathematics for undergraduates.
Teaching, some selected courses
NTU, Singapore, 2014, Semester 2: Topics in Applied and Discrete Mathematics (undergraduate/graduate seminar).
NTU, Singapore, 2010–2012, Semester 1: "It's a Discreetly Discrete World."
NTU, Singapore, 2010, Semester 2: Discrete Methods (graduate course), MAS 711.
NTU, Singapore, 2009, Semester 1: Real Analysis I, MAS 311.
NTU, Singapore, 2009, Semester 2: Topics in Number Theory III: Discrete Geometry and Number Theory, MAS 742.
NTU, Singapore, 2008, Semester 1: Graph Theory, MAS 324.
NTU, Singapore, 2008, Semester 2: Discrete Mathematics with Elementary Number Theory, MAS 214 (158 students).
MSRI/BIRS, Banff, Canada, 2005: two-week summer course for 40 graduate students, co-taught with Matthias Beck.
Temple University: Number Theory (PhD level); Analytic Number Theory; Algebraic Number Theory; Number Theory (undergraduate).
Temple University: Combinatorial Geometry, based on Computing the Continuous Discretely (with Matthias Beck, Springer UTM series).
Temple University: Discrete Geometry; Combinatorial Topology and Knots.
Temple University: Cryptography and Information Theory for IST majors (undergraduate).
Temple University: Calculus I, II, III; Analysis; Differential Equations; For All Practical Purposes (for non-majors).
UC San Diego, 1995–1996: Calculus for the Life Sciences I, II, III.
University of Northern Colorado: Calculus I, II, III; Real Variables I, II; Linear Algebra; Abstract Algebra (master's level); Analytic Number Theory.
University of Northern Colorado: Seminar in Number Theory; Topics in Finite Mathematics; Seminar on Mathematical Discovery using Pólya's books.
University of Northern Colorado: History of Mathematics; Math for Elementary School Teachers; Math for the Liberal Arts.
Postdocs
Romanos Malikiosis, Nanyang Technological University, Singapore, 2012–2014.
Christian Tafula, University of São Paulo, 2025–2028.
PhD Students
Matthias Beck, Temple University, PhD 2000: Arithmetic properties of rational polytopes.
David DeSario, Temple University, PhD 2007: Polyhedral theta functions and their applications to combinatorial geometry.
Wang Xinli, Nanyang Technological University, Singapore, PhD 2012 (co-supervised with Prof. Chee): Discrete-geometric functions associated to polyhedral cones and point sets.
Fabrício Caluza Machado, University of São Paulo, PhD 2021: Applications of harmonic analysis to discrete geometry.
Michel Faleiros, University of São Paulo, in progress.
Undergraduate Thesis Students
Czarina Ann Marifosque, Nanyang Technological University, 2008.
Nhat Le Quang, Nanyang Technological University, 2009.
Stephanie Gabriela, Nanyang Technological University, 2009.
Danh Nguyen Luu, Nanyang Technological University, 2011.
Yichi Zhang, Nanyang Technological University, 2012–2013.
André Rosenbaum, University of São Paulo, in progress.
Caio Simon de Oliveira, University of São Paulo, in progress.
Master’s Students
Ana Carolina Laurini Malera, University of São Paulo, in progress.
Tiago Royer, University of São Paulo, 2018.
Gervasio Santos, University of São Paulo, 2018.
Pan Ying, Nanyang Technological University, Singapore, 2013.
Yudistira Mulyadi, Nanyang Technological University, Singapore, 2012.
Jessica Cuomo, Temple University, 2006: Laplacians of some planar graphs and their eigenvalues.
Neal Weikel, Temple University, 2006: Linear programming and its applications to the real estate market.
Wayne Haga, University of Northern Colorado, 1996.
David Auter, University of Northern Colorado, 1996.
Matt Isom, University of Northern Colorado, 1995.
Patrick Wahl, University of Northern Colorado, 1994.
Service to the Mathematical Community
Deputy Director, ICERM (Institute for Computational and Experimental Research in Mathematics), Brown University, 2015–2017.
Faculty leader, Summer@ICERM 2014 undergraduate research program, Providence, RI, June 16–August 8, 2014.
Co-chair, three-month program on inverse moment problems, Institute for Mathematical Sciences, Singapore, November 18, 2013–January 25, 2014.
Founding and Managing Editor, Online Journal of Analytic Combinatorics (with Alex Iosevich and Izabella Łaba), 2005–present: open access, free of charge, and rigorously refereed.
Editor, The Ramanujan Journal, 2012–present.
NSF review panel for Combinatorics and Discrete Mathematics grants, Washington, DC, August 2007.
Co-organizer with Matthias Beck, MSRI/BIRS summer course for 40 graduate students, Banff, Canada, August 2005.
Local organizer, Marvin Fest, a conference honoring Marvin Knopp's 73rd birthday, Philadelphia, January 2006.
Founder and organizer, Discrete Mathematics Seminar, Temple University, 2006.
Founder, Society for Undergraduate Mathematics, Temple University, 1999.
Putnam exam facilitator and coach, Temple University, several years.
Writer for the Temple Undergraduate Mathematics Monthly.
Mentored and supervised PhD and master's students at the University of Northern Colorado and Temple University, and mentored undergraduate research projects in combinatorics and number theory.
Taught and developed about 70 undergraduate and graduate courses, including discrete mathematics, combinatorics, number theory, differential equations, Fourier analysis, linear algebra, abstract algebra, and real and complex analysis.
Served on hiring, graduate, undergraduate, colloquium, and university senate committees.
Reviewer for Mathematical Reviews.
Referee for numerous journals, including Inventiones Mathematicae, Journal für die reine und angewandte Mathematik, Mathematische Annalen, Transactions of the AMS, Journal of Combinatorial Theory, Series A, Bulletin of the London Mathematical Society, Advances in Applied Mathematics, American Mathematical Monthly, Discrete & Computational Geometry, Electronic Journal of Combinatorics, Experimental Mathematics, and Journal of Number Theory.
Service to the Division of Mathematical Sciences, NTU, Singapore
Member, Executive Committee of the Division of Mathematical Sciences, 2008–2014.
Member, Committee on Promotion and Tenure, 2009–2014.
Coordinator, SM bridging program with China, 2009–2014.
Hiring Committee, 2008 and 2011–2013.
Chair, Final Year Project Committee, 2009–2012.
Chair, Outreach Committee, 2010–2012.
Chair, Academic Committee (curriculum reform and undergraduate teaching), 2008.
Member, Outreach Committee, School of Physical and Mathematical Sciences (SPMS), 2008.
Mentor and Final Year Project supervisor for five students, 2008–2012.
Speaker, 3rd Mathematics Workshop for Malaysian Teachers, March 2014.
Grader, NTU Mathematics Competition, April 2014.
Judge, Singapore High School Mathematics Competition, 2008, 2010, and 2012.
Executive Committee, Singapore International Mathematical Modelling Competition, April 2008.
Supervised and traveled with the NTU team to the International Mathematics Competition (IMC), Bulgaria, 2008.
Organizing Committee, "Advances in Mathematics" conference for the grand opening of SPMS, July 20–22, 2009.
Interviewer, Lee Kuan Yew Postdoctoral Fellowships, 2009.
Selected Invited Talks
Invited speaker, Purdue University: "PL homeomorphisms and related topics, revisiting the work of Peter Greenberg," 2026.
Colloquium, University of Virginia: "The Geometry of Numbers, Tilings, and Fourier Transforms," 2025.
Special session in Harmonic Analysis, Mathematical Congress of the Americas (MCA 2025), Miami, Florida: "Multi-tilings and the Geometry of Numbers, via the Siegel–Bombieri Approach," 2025.
Invited short course, University of Lisbon, Portugal: "Introduction to Fourier Methods for Polytopes and Cones," 2024.
Plenary talk, conference in honor of Nicolau Saldanha's 60th birthday, Pontifical Catholic University of Rio de Janeiro (PUC-Rio): "Multi-tilings and the Geometry of Numbers, Using the Siegel–Bombieri Approach," 2024.
Plenary lecture, 1st Brazilian Workshop in Analytic Number Theory, IMPA, Rio de Janeiro: "Multi-tilings and the Geometry of Numbers, Using the Siegel–Bombieri Approach," 2024.
Colloquium, Pontifical Catholic University of Chile, Santiago: "The Geometry of Numbers, and an Extension of the Bombieri–Siegel Formula," 2023.
Invited seminar, Combinatorial and Additive Number Theory (CANT), New York Number Theory Seminar: "The Covariogram and an Extension of Siegel's Formula," 2022.
Colloquium, State University of Campinas (UNICAMP): "The Fourier Transform of a Polytope and Its Applications in Discrete Geometry," 2018.
Invited short course, São Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization: "Harmonic Analysis on Polytopes and Cones," 2016.
Combinatorics seminar, Massachusetts Institute of Technology (MIT): "Translational Tiling by Convex Objects," 2015.
Combinatorics seminar, Princeton University: "Translational Tilings and Multi-Tilings by Convex Polytopes," 2015.
Colloquium, Tulane University, New Orleans: "Multi-tiling Euclidean Space by Using Translated Polytopes," 2015.
Combinatorics seminar, University of Rochester: "Translations of Convex Bodies and Multi-tilings," 2015.
Number theory seminar, Amherst College: "Cone Theta Functions, and Rationality of Spherical Volumes," 2015.
Colloquium, Claremont McKenna College: "Translational Tilings," 2015.
Colloquium, University of Florida: "Cone Theta Functions and Rationality of Spherical Volumes," 2015.
Combinatorics seminar, Yale University: "Cone Theta Functions," 2014.
Number theory seminar, Brown University: "More Details on the Cone Theta Functions and Rationality of Spherical Volumes," 2014.
Colloquium, Brown University: "Cone Theta Functions and What They Tell Us About the Rationality of Spherical Volumes," 2014.
Geometry and topology seminar, Brown University: "Multiply Tiling Euclidean Space by Translations of a Convex Polytope," 2014.
Plenary speaker, Erwin Schrödinger Institute workshop "Minimal Energy Point Sets, Lattices and Designs," Vienna: "Cone Theta Functions and Rationality of Volumes of Spherical Polytopes," 2014.
ICERM research program "Challenges in 21st Century Experimental Mathematical Computation," Providence: "Equality of Dedekind Sums: Experimental Data and Theory," July 2014.
Colloquium, University of Queensland, Australia: "Multiple Tilings of Euclidean Space by Translations of a Convex Polytope," 2014.
Additive combinatorics seminar, École Polytechnique, Paris: "Multiple Tilings of Euclidean Space by Translations of a Convex Body," November 2013.
Seminar, TU Berlin, Germany: "Multiply Tiling Euclidean Space by Translating a Convex Object," November 2013.
Colloquium, Magdeburg University, Germany: "Multiply Tiling Euclidean Space by Translating a Convex Object," November 2013.
GeoLMI 2013, conference in honor of Jean Bernard Lasserre's 60th birthday, CIRM Luminy, France: "A Fourier Approach to the Brion Identities," November 2013.
Seminar, University of Western Australia, Perth: "Multiple Tilings of Euclidean Space by Translations of a Convex Body," October 2013.
Number theory special session, 57th Annual Meeting of the Australian Mathematical Society, Sydney: "Tiling the Integer Lattice with Translated Integer Sublattices," October 2013.
Down Under Number Theory Workshop, Newcastle, Australia: "Multiple Tilings of Euclidean Space by Translations of a Convex Polytope," October 2013.
Fourier workshop, Budapest: "Tiling the Integer Lattice with Translated Integer Sublattices," September 2013.
Number theory seminar, Université de Bordeaux, France: "Cone Theta Functions and What They Tell Us About Irrational Volumes of Spherical Polytopes," June 2013.
Colloquium, Paul Sabatier University, Toulouse, France: "Translational Tilings by a Convex Polytope, a Combinatorial and Harmonic Analysis Perspective," May 2013.
Combinatorics seminar, Oxford University (London Mathematical Society visiting grant): "Multiple Tilings by a Convex Body," October 2012.
Combinatorics seminar, Cambridge University (London Mathematical Society visiting grant): "Multiple Tilings by a Convex Body," October 2012.
Colloquium, University College London (London Mathematical Society visiting grant): "Multiple Tilings by a Convex Body," October 2012.
Plenary speaker, Mathematical Society of the Philippines Annual Convention, Lipa City: "Tilings by Translations of a Convex Body, with Multiplicity," 2012.
International Number Theory Conference in memory of Alf van der Poorten, University of Newcastle, Australia: "Conic Theta Functions and Their Relations to Classical Theta Functions," 2012.
Colloquium, University of Queensland, Australia: "Multiple Tilings of Euclidean Space by Translations of a Convex Body," 2012.
Colloquium, Hong Kong University of Science and Technology: "Tiling Euclidean Space by Translations of a Convex Polytope," 2012.
NTU–Tsinghua University joint workshop, Beijing: "Tilings and Multi-tilings," 2012.
Seminar, University of Auckland, New Zealand: "Translational Tilings of a Convex Body, with Multiplicity," 2011.
Seminar, Alfréd Rényi Institute of Mathematics, Budapest: "Integer Lattice Extensions of Erdős' Classic Problem of Tiling the Integers by Arithmetic Progressions," 2011.
Workshop on Mathematical Crystallography (MaThCryst), Manila, Philippines: "Translational Tilings of a Convex Body, with Multiplicity," 2011.
Clifford Lecturer, Tulane University: "Towards an Ehrhart Theory for Real Polytopes," March 2010.
AMS special session on Algebra and Number Theory with Polyhedra, San Francisco State University: "Tiling Lattices with Sublattices," April 2009.
Number theory seminar, National University of Singapore: "Hecke Operators on Hypergeometric Functions," 2009.
"The Mathematical Interests of Peter Borwein," IRMACS Centre, Simon Fraser University, Canada: "New Measures of Discrete Volumes for Polytopes Whose Vertices Have Arbitrary Real Coordinates," May 2008.
AMS special session on Combinatorial Enumeration, Optimization, Geometry, and Statistics, Tennessee: "A Solid Angle Theory for Real Polytopes," November 2007.
Colloquium, Tulane University: "Computing Solid Angles and Discrete Volumes of Polytopes," October 2007.
Number theory seminar, Stanford University: "Theta Functions for Cones and Relations Between Solid Angles for Polytopes," 2007.
AMS special session on Experimental Mathematics, National AMS Meeting, New Orleans: "Extending the Solid Angle Relations of Polytopes," January 2007.
AMS special session on Algebraic and Analytic Combinatorics, AMS Fall Eastern Meeting, University of Connecticut: "Polyhedral Theta Functions," October 2006.
Discrete Mathematics Day, SUNY Binghamton: "A New Approach to Integer Linear Programming," May 2006.
Google Tech Talk, Googleplex, Bay Area Discrete Math Day XII: "Integer Linear Programming, a New Approach," April 2006.
Colloquium, University of Florida: "Integer Linear Programming Using Differentiable Dedekind Sums," February 2006.
Conference on Modular Forms and Related Topics in honor of Marvin Knopp's 73rd birthday: "Integer Linear Programming via Analytic Number-Theoretic Functions Called Differentiable Dedekind Sums," January 2006.
Colloquium, Cal Poly: "Differentiable Dedekind Sums in Integer Linear Programming," 2005.
Clifford Lecturer, Tulane University: "A Different Approach to Integer Linear Programming, Using Dedekind-Like Sums," 2005.
Euroconference on Algebraic and Geometric Combinatorics, University of Crete: "Using Differentiable Dedekind Sums," 2005.
Combinatorial and Additive Number Theory (CANT) conference, CUNY Graduate Center: "Weighted Lattice Point Enumeration, and Dedekind Sums," 2005.
Colloquium, University of Maryland: "Traditional Dedekind Sums and New Polynomial Dedekind Sums for Weighted Lattice Point Enumeration in Polytopes," 2004.
Workshop on Analytic and Computational Number Theory, Dalhousie University, Halifax, Canada: "Hecke Operators on Rational Functions," 2004.
Combinatorics seminar, University of Michigan: "Solid Angles, and Theta Functions on Polytopes," 2003.
Integer Points Conference, Utah: "A Decomposition of Quasipolynomials into Eigenspaces of Hecke Operators," summer 2003.
Colloquium, Brown University: "Zeta Functions for Polyhedral Cones, Functional Equations, and Extended Lipschitz Summation Formulas for Cones," 2003.
IDA Colloquium, Institute for Defense Analyses, Princeton: "Hecke Operators on Rational Functions," 2003.
Pacific Institute for the Mathematical Sciences (PIMS), Simon Fraser University, Canada: "Texture Maps in Image Processing and Their Links to Analytic Number Theory and Combinatorial Geometry," 2003.
Discrete and computational geometry seminar, Courant Institute: "Solid Angles of Polytopes and Solid Angle Polynomials Attached to Polytopes," 2002.
Colloquium, Tulane University: "Zeta Functions for Polyhedral Cones in ℝᵈ Have a Functional Equation," 2002.
Number theory seminar, University of California, Santa Barbara: "An Extension of the Hurwitz Zeta Function for Polyhedral Cones," 2002.
Number theory seminar, University of California, San Diego: "An Extension of the Hurwitz Zeta Function for Polyhedral Cones in ℝᵈ," 2002.
Number theory seminar, University of California, Santa Cruz: "Zeta Functions for Cones," 2002.
Special session, first joint meeting of the American Mathematical Society and the French Mathematical Society, France: "The Frobenius Coin Exchange Problem: A Blend of Combinatorics, Number Theory, and Fourier Analysis," 2001.
AMS special session, sectional meeting, Providence, Rhode Island: "The Frobenius Coin Exchange Problem, Rational Polytopes, and Fourier-Dedekind Sums," 1999.
AMS special session, University of Florida: "A Simple Proof of Riemann's Functional Equation for the Zeta Function," 1999.
MSRI conference in combinatorial geometry, Berkeley: "The Ehrhart Polynomial of a Lattice Polytope," 1997.
Special session, Joint Mathematics Meetings (AMS), Orlando, Florida: "The Ehrhart Polynomial of a Lattice Polytope," January 1996.
Personal Information
Citizenship: United States.
Email: sinai.robins@gmail.com
Languages: Fluent in English and Hebrew; reading knowledge of French and Spanish.
Skills: Communication, grant writing, student mentoring, and collaborative research with colleagues across many countries.
Hobbies
I enjoy classical piano, creative writing, hiking, Latin dancing, running, rollerblading, weight lifting, sketching and oil painting, and traveling the globe. Above all, I love doing mathematics with friends at the local coffee house.