About

Martin Kassabov is a professor in the Department of Mathematics at Cornell University. He holds an M.Sc. from Sofia University (1998) and a Ph.D. from Yale University (2003). His research interests primarily focus on the representation theory of discrete groups, with particular emphasis on Kazhdan property and property tau, which have numerous applications in combinatorics. A significant part of his work involves properties T and tau, arising from the representation theory, and their applications in combinatorics. Additionally, his research encompasses combinatorial algebra, concentrating on topics such as automorphism groups, Golod-Shafarevich groups, and group rings.

Research topics

• Mathematics
• Artificial Intelligence
• Computer Science
• Algorithm
• Discrete mathematics
• Combinatorics

Selected publications

• Examples of finitely presented groups with strong fixed point properties and property (T)

  Open MIND · 2026-01-30

  preprintSenior author

  We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the simplicity requirement.

  DOI

• Examples of finitely presented groups with strong fixed point properties and property (T)

  ArXiv.org · 2026-01-30

  articleOpen accessSenior author

  We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the simplicity requirement.

  PublisherOA PDF

• Expander graphs are globally synchronizing

  Advances in Mathematics · 2026-01-19 · 2 citations

  preprintOpen access
  PublisherOA PDFDOI

• Expander graphs are globally synchronizing

  Advances in Mathematics · 2026-01-19

  article
  PublisherDOI

• Groups with property (T) and many alternating group quotients

  Groups Geometry and Dynamics · 2025-08-01

  articleOpen accessSenior author

  We prove that, for the free algebra over a sufficiently rich operad \mathcal{O} , a large subgroup of its group of tame automorphisms has Kazhdan’s property (T). We deduce that there exists a group with property (T) that maps onto large powers of alternating groups.

  PublisherOA PDFDOI

• Detecting null patterns in tensor data

  arXiv (Cornell University) · 2024-08-30

  preprintOpen access

  This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor decompositions, and Tucker decompositions. It also includes a new family of null patterns -- not known to be detectable by current methods -- that can be thought of as continuous decompositions approximating curves and surfaces. We present a general algorithm to detect null patterns in each class using a parameter we call a \textit{chisel} that tunes the search to patterns of a prescribed shape. We also show that the patterns output by the algorithm are essentially unique.

  PublisherOA PDFDOI

• Monotone parameters on Cayley graphs of finitely generated groups

  arXiv (Cornell University) · 2024-04-16

  preprintOpen access1st authorCorresponding

  We construct a new large family of finitely generated groups with continuum many values of the following monotone parameters: spectral radius, critical percolation, and asymptotic entropy. We also present several open problems on other monotone parameters.

  PublisherOA PDFDOI

• Symmetric Polynomials in Free Associative Algebras—II

  Mathematics · 2023-11-29

  articleOpen accessSenior author

  Let K⟨Xd⟩ be the free associative algebra of rank d≥2 over a field, K. In 1936, Wolf proved that the algebra of symmetric polynomials K⟨Xd⟩Sym(d) is infinitely generated. In 1984 Koryukin equipped the homogeneous component of degree n of K⟨Xd⟩ with the additional action of Sym(n) by permuting the positions of the variables. He proved finite generation with respect to this additional action for the algebra of invariants K⟨Xd⟩G of every reductive group, G. In the first part of the present paper, we established that, over a field of characteristic 0 or of characteristic p>d, the algebra K⟨Xd⟩Sym(d) with the action of Koryukin is generated by (noncommutative version of) the elementary symmetric polynomials. Now we prove that if the field, K, is of positive characteristic at most d then the algebra K⟨Xd⟩Sym(d), taking into account that Koryukin’s action is infinitely generated, describe a minimal generating set.

  PublisherOA PDFDOI

• Tame automorphism groups of polynomial rings with property (T) and infinitely many alternating group quotients

  Transactions of the American Mathematical Society · 2023 · 2 citations

  Senior authorCorresponding
  • Artificial Intelligence
  • Computer Science
  • Algorithm

  We construct new families of groups with property (T) and infinitely many alternating group quotients. One of those consists of subgroups of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal u normal t left-parenthesis bold upper F Subscript p Baseline left-bracket x 1 comma ellipsis comma x Subscript n Baseline right-bracket right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">F</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">[</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo> … </mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy="false">]</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {Aut}(\mathbf {F}_{p}[x_1, \dots , x_n])</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by a suitable set of tame automorphisms. Finite quotients are constructed using the natural action of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal u normal t left-parenthesis bold upper F Subscript p Baseline left-bracket x 1 comma ellipsis comma x Subscript n Baseline right-bracket right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">F</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">[</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo> … </mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo stretchy="false">]</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathrm {Aut}(\mathbf {F}_{p}[x_1, \dots , x_n])</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -dimensional affine spaces over finite extensions of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper F Subscript p"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="bold">F</mml:mi> </mml:mrow> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mathbf {F}_p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . As a consequence, we obtain explicit presentations of Gromov hyperbolic groups with property (T) and infinitely many alternating group quotients. Our construction also yields an explicit infinite family of expander Cayley graphs of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4"> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding="application/x-tex">4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for alternating groups of degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Superscript 7 Baseline minus 1"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>p</mml:mi> <mml:mn>7</mml:mn> </mml:msup> <mml:mo> − </mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">p^7-1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for any odd prime <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding="application/x-tex">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .

  PublisherOA PDFDOI

• Property (T) and Many Quotients

  arXiv (Cornell University) · 2023-08-28

  preprintOpen accessSenior author

  We prove that, for the free algebra over a sufficiently rich operad, a large subgroup of its group of tame automorphisms has Kazhdan's property (T). We deduce that there exists a group with property (T) that maps onto large powers of alternating groups.

  PublisherOA PDFDOI

Recent grants

• Properties T, Tau and Kazhdan constants

  NSF · $105k · 2006–2009

• Representation Theory of Groups and Applications

  NSF · $194k · 2013–2016

• Properties T, Tau and pro-finite groups

  NSF · $196k · 2009–2014

• Representation Theory of Groups and Applications

  NSF · $229k · 2016–2019

Frequent coauthors

• Francesco Matucci

  35 shared

• Collin Bleak

  21 shared

• Andrei Jaikin‐Zapirain

  18 shared

• William M. Kantor

  15 shared

• Nikolay Nikolov

  University of Oxford

  12 shared

• Robert M. Guralnick

  Walter de Gruyter (Germany)

  11 shared

• Alexander Lubotzky

  Courant Institute of Mathematical Sciences

  10 shared

• Tim Riley

  Cornell University

  9 shared

Awards & honors

• Twelve new Klarman Fellows to pursue innovative, timely rese…