Leonid Monin

I am currently a Bernoulli instructor at EPFL. Before that I was a postdoc working at the Max Planck Institute for Mathematics in the Sciences in Leipzig and at the University of Bristol. In 2019 I obtained my PhD at the University of Toronto where I worked with Askold Khovanskii, here is my CV.

You can reach me via my email: leonid.monin@epfl.ch. You might be interested in AdIMOM and our homemade seminars.

Research

I am interested in several areas between algebra and geometry. More specifically, my research can be broadly divided into two parts. The first part is combinatorial algebraic geometry and the second one is Teichmüller theory and moduli spaces. In combinatorial algebraic geometry I am mostly interested in Newton polyhedra theory, toric varieties, enumerative geometry, spherical varieties, and tropical geometry. In Teichmüller theory I am mostly interested in counting problems, geometry of Teichmüller space equipped with Thurston metric, and dilation surfaces.

My publications and preprints:

(with J. Lindberg and K. Rose) A polyhedral homotopy algorithm for computing critical points of polynomial programs, submitted 2023 [pdf]
(with L. Kühne) Faces of cosmological polytopes, submitted 2022 [pdf]
(with P. Breiding, M. Michalek, and S. Telen) The Algebraic Degree of Coupled Oscillators, submitted 2022 [pdf]
(with A. Khovanskii) Gorenstein algebras and toric bundles, submitted 2021 [pdf]
(with E. Duryev) Billiards and hyperelliptic curves with many automorphisms, submitted 2021 [pdf]
(with Y. Cid-Ruiz and F. Mohammadi) Multigraded algebras and multigraded linear series, submitted 2021 [pdf]
(with L. Manivel, M. Michalek, T. Seynnaeve, and M. Vodicka) Complete quadrics: Schubert calculus for Gaussian models and semidefinite programming, Journal of the European Mathematical Society 2023 [pdf]
(with A. Khovanskii and I. Limonchenko) Generalized virtual polytopes and quasitoric manifolds, Trudy MIAN 2023 [pdf]
(with A. Khovanskii and I. Limonchenko) Cohomology rings of quasitoric bundles, Filomat 2023 [pdf]
(with F. Mohammadi and M. Parisi) Triangulations and Canonical Forms of Amplituhedra: a fiber-based approach beyond polytopes, Communications in Mathematical Physics 2021 [pdf]
(with J. Hofscheier and A. Khovanskii) Cohomology of toric bundles and rings of conditions of horospherical varieties, accepted to Arnold Mathematical Journal 2020 [pdf]
(with M. Michalek and J. Wisniewski) Maximum likelihood degree, complete quadrics and \(\mathbb{C}^*\)-action, SIAM Journal on Applied Algebra and Geometry (SIAGA), 2021 [pdf]
(with R. Cavalieri and M. Gillespie) Projective Embeddings of \(\overline{M_{0,n}}\) and Parking Functions, accepted to Journal of Combinatorial Theory, Series A, 2021 [pdf]
Overdetermined collections of linear series on toric, spherical, and other algebraic varieties, Advances in Mathematics 2020 [pdf]
(with V. Telpukhovskiy) On normalizations of Thurston measure on the space of measured laminations, Topology and its Applications 2019 [pdf]
(with J. Rana) Equations of \(\overline{M_{0,n}}\), in "Combinatorial Algebraic Geometry” Edited by Gregory G. Smith and Bernd Sturmfels 2017 [pdf]
Discrete Invariants of Generically Inconsistent Systems of Laurent Polynomials, Mathematical Reports of the Academy of Science of the Royal Society of Canada, 2017 [pdf]
(with A. Khovanskii) The Resultant of Developed Systems of Laurent Polynomials, Moscow Mathematical Journal, 2017 [pdf]
Lattice Geometry and Reduction of Finitely Generated Abelian Groups to a Normal Form, Mathematical Reports of the Academy of Science of the Royal Society of Canada, 2014 [pdf]

Work in progress:

(with A. Khovanskii) BKK theorem for T-varieties and the ring of conditions of horospherical homogeneous spaces.
(with L. Bossinger and A. Nájera Chávez) Mirror symmetry for homogeneous spaces.
Weighted counting of mapping class group orbits of geodesic currents.
(with E. Smirnov) Polyhedral models for K-theory of toric and flag varieties.
(with A. Khovanskii) Toric bundles over toric varieties.

Teaching

I am not teaching at the moment, earlier I taught the following courses:

at University of Bristol:

Fall 2019: Instructor for Reading course on Combinatorial algebraic geometry

at University of Toronto:

Instructor and the course coordinator:
Spring 2019: course MAT 401 Polynomial equations and Fields. Here are some materials.
Summer 2018: MAT136 Calculus I (B)

2013-2018: TA for MAT333 Topology, MAT257 Analysis II, MAT402 Classical Geometries, MAT186 Calculus I, MAT332 Graph Theory, MAT135 Calculus I (A), MAT136 Calculus I (B).

at Independent University of Moscow:

2012-2013: TA for Geometry I, Topology I.

at Higher School of Economics:

2011-2013: TA for Game Theory, Mathematical Introduction into Economic, Basic Mathematical Model of Political Economics, Discrete Mathematics.

Last updated: Back to top ⇧