Ilia Nekrasov

Symmetric Tensor Categories and Model Theory

• Upper bounds for measures on distal classes [ArXiv]
  joint with A. Snowden
  Submitted

• Arboreal tensor categories [ArXiv]
  joint with A. Snowden and N. Harman
  Selecta Math. (N.S.) 31 (2025), no. 58

• Tensorial Measures on Omega-Categorical Structures
  Ph.D. Thesis
  Repository Link 

Classification of Overgroups in Lie Groups

• Overgroups of exterior powers of an elementary group. Normalizers [ArXiv]
  joint with R. Lubkov
  Documenta Math. 29 (2024), no. 5

• Overgroups of exterior powers of an elementary group. Levels [ArXiv]
  joint with R. Lubkov
  Linear and Multilinear Algebra, 72 (2024), no. 4

• Explicit equations for exterior square of the general linear group [ArXiv]
  joint with R. Lubkov
  J Math Sci 243 (2019)

Equivariant Noetherianity of Algebraic Spaces

• Dual Infinite Wedge is GL_{\infty}-equivariantly noetherian [ArXiv]

Compactifications of M_{0,n}, Alexander self-dual complexes, and Polygon Spaces

• Compactifications of M_{0,n} associated with Alexander self-dual complexes: Chow ring, ψ-classes and intersection numbers [ArXiv]
  joint with G. Panina
  Proc. Steklov Inst. Math. 305 (2019)

• Geometric presentation for the cohomology ring of polygon spaces [ArXiv]
  joint with G.Panina
  St. Petersburg Math. J. 31 (2020)

• Intersection numbers of Chern classes of tautological line bundles on the moduli spaces of flexible polygons [ArXiv]
  joint with G. Panina and A. Zhukova

• Alexander r-tuples and Bier complexes [ArXiv]
  joint with G. Panina,  D. Jojić, and R. Živaljević
  Publications de l'Institut Mathematique 104 (2018), issue 118

Cyclopermutohedron

• Cyclopermutohedron: geometry and topology [ArXiv]
  joint with G. Panina and A. Zhukova
  European Journal of Mathematics 2 (2016)

• Volume and lattice points counting for the cyclopermutohedron [ArXiv]
  joint with G. Panina

Formal Modules and Arithmetic in Local Fields

• Cohomology of Formal Modules over Local Fields
  joint with S. Vostokov
  Math Notes 105 (2019)

• Explicit constructions and arithmetic of local number fields
  joint with S.Vostokov, S. Afanaseva, M. Bondarko, V. Volkov, O. Demchenko, E. Ikonnikova, I. Zhukov, P. Pital’
  Vestnik of Saint Petersburg University 4 (2017), no. 3

• Lutz filtration as a Galois module
  joint with S. Vostokov and R. Vostokova
  Lobachevskii J Math 37 (2016)

• The Lubin–Tate Formal Module in a Cyclic Unramified p-Extension as a Galois Module
  joint with S. Vostokov
  J Math Sci 219 (2016)

Below is information on recent courses I have taught. Other pedagogical and instructional roles, including course coordination, can be found in CV.

Algebra

• Honors Introduction to Abstract Algebra
  Upper-division undergraduate course・Lecture-based with in-depth homework assignments
  We covered core and intermediate topics from group theory and ring theory. Highlights includes the Sylow theorems in the structure theory of finite groups, the ping-pong lemma in group actions, the classification of finitely generated abelian groups via modules over principal ideal domains, and ideal-theoretic perspectives on the Fundamental Theorem of Arithmetic.
  Mainly, we used Abstract Algebra by T. Judson and Algebra: Chapter 0 by P. Aluffi.
  Canvas link(s): Fall2025

• Introduction to Abstract Algebra
  Upper-division undergraduate course・Lecture-based
  We covered core topics from group theory, ring theory, and theory of fields. Highlights includes the classification of finite abelian groups, Burnside’s lemma in group actions, the Fundamental Theorem of Arithmetic for principal ideal domains and its extension to ideal factorization, and an introduction to splitting fields.
  Mainly, we used Abstract Algebra by T. Judson.
  Canvas link(s): Fall2024, Spring2024

Analysis

• Introduction to Complex Analysis
  Upper-division undergraduate course・Lecture-based
  We covered core topics in the theory of analytic functions and the calculus of residues, with the exposition taking a more geometric perspective than the standard analytic approach. Along the way, we introduced the Riemann sphere as a complex manifold and developed holomorphic and meromorphic functions, as well as differential forms, on the complex plane and on the Riemann sphere. Highlights included Cauchy’s theorems, residue theory on the Riemann sphere, the theory of Möbius transformations of the Riemann sphere, and their use in complex integrals.
  Mainly, we used Basic Complex Analysis by J. Marsden and M. Hoffman.
  Canvas link(s): Fall2025, Spring2026

• Calculus II
  Lower-division undergraduate course・Active-learning

The course was focused on the definite integral and its interpretations, techniques for constructing antiderivatives, and methods of integration, including substitution, integration by parts, trigonometric substitutions, and improper integrals. Applications of integration included area and volume, physical and geometric applications, probability and distributions, and numerical integration. The course concluded with sequences and series, covering convergence tests, power series, and Taylor polynomials and series as tools for function approximation.
We used Calculus: Single Variable by W. McCallum, D. Hughes-Hallett, A. Gleason.
Canvas link(s): Spring2022, Fall2019

• Calculus I
  Lower-division undergraduate course・Active-learning
  The course covered foundational topics in differential and integral calculus. Specifically, we studied functions and limits, continuity, and the derivative as a rate of change, followed by techniques of differentiation and the Mean Value Theorem. Applications of derivatives included optimization, related rates, and curve sketching. The course concluded with an introduction to the definite integral, its interpretation via the Fundamental Theorem of Calculus, and basic techniques for constructing antiderivatives.
  We used Calculus: Single Variable by W. McCallum, D. Hughes-Hallett, A. Gleason.
  Canvas link(s): Fall2022, Winter2022, Fall2020, Winter2019, Fall2018

Note for Students: If you are interested in a reading course or a similar independent study, email me!
Working in a small group (for example, with a classmate) is often even more productive.

Reading Courses

• Model Theory and Combinatorics of Oligomorphic Groups
  In-depth analysis of combinatorial and model-theoretic structures related to actions of oligomorphic groups.
  We mainly used Oligomorphic Permutation Groups and Permutation Groups by P. Cameron.

• Introduction to Representation Theory
  Course covers core ideas of representation theory of finite groups over characteristic zero. We usually go over Linear Representations of Finite Groups by Jean-Pierre Serre with a plethora of exercises/problems exploring representations of abelian, symmetric, and dihedral groups.

• Introduction to Local Number Theory
  Course mainly followed A Classical Introduction to Modern Number Theory by K. Ireland and M. Rosen with special emphasize on Reciprocity Laws.

Honors and Master Theses

• Categorification and Combinatorics of Oligomorphic Groups
  Expected Spring 2026.

• Lubin–Tate extensions and Carlitz module over a projective line
  Nikita Elizarov, Universität Bielefeld, successfully defended his Master’s thesis, which subsequently resulted in a publication.

Other Advising and Mentoring activities can be found in my CV.

You can contact me via email at ilianekrasov@berkeley.edu or find me in Evans Hall 791. 

Correspondence should be addressed to:

Department of Mathematics

970 Evans Hall, MC 3840

Berkeley, CA 94720-3840