Katalin Berlow

Research

My research focuses on descriptive combinatorics and measured group theory with applications to ergodic theory and geometric group theory. I work with the broader goal of understanding how combinatorial structure encodes dynamical and group-theoretic information.

Papers in Preparation

• Separating Complexity Classes of LCL Problems on Grids, Part 2
  with Anton Bernshteyn, Clark Lyons, Felix Weilacher
  [In preparation]
• Equivalence Relations Acting on Bundles of Trees
  with Ronnie Chen, Robin Tucker-Drob, Anush Tserunyan
  [In preparation]

Papers (Graduate School)

• Separating Complexity Classes of LCL Problems on Grids
  with Anton Bernshteyn, Clark Lyons, Felix Weilacher
  [arXiv] [Slides]
• Borel Polychromatic Number of Grids
  with Edward Hou
  [arXiv]

Papers (Undergraduate)

• Intersection Bodies of Polytopes
  with Marie Brandenburg, Chiara Meroni, Isabelle Shankar
  [arXiv] [Journal]
• Restricted Stacks as Functions
  [arXiv] [Journal] [Slides]
• Almost Abelian Lie Groups, Subgroups, and Quotients
  with Marcelo Almora Rios, Zhirayr Avetisyan, Isaac Martin, et al.
  [arXiv] [Journal]

Talks

Invited talks and Workshops

• TBD
  Joint Mathematics Meetings, Chicago, IL, January 2027.
• Workshop on group actions and equivalence relations
  Budapest, Hungary, July 2026.
• Local Problems on Grids: FIID/FFIID Separations and a Failure of Baire Shift Universality
  Caltech Logic Seminar, Apr 15, 2026.
• Measurable analog of Euler’s formula for pmp graphs
  UT Austin Groups and Dynamics Seminar, Austin, TX, Mar 25, 2026.
• Borel combinatorics on grids
  AMS Spring Western Sectional Meeting, Boise, Idaho, Mar 7–8, 2026.
• Borel combinatorics on grids
  ELTE Borel Combinatorics Seminar, Budapest, Hungary, Feb 25, 2026.
• LCLs on Grids
  Drafting Workshop in Discrete Mathematics, Number Theory and Probability, Budapest, Jan 2026.
• Borel combinatorics on grids
  North American Descriptive Set Theory, University of Maryland, Oct 2025.
• Separating Complexity Classes of LCLs on Grids
  CanaDAM, Ottawa, May 2025.
• Separating Complexity Classes of LCLs on Grids
  Southeastern Logic Symposium (SEALS), University of Florida, Mar 2025. [Slides]

Expository

Here are some expository documents I have written:

• Amenable Groups Acting on Trees
  [Notes]

Teaching

Instructor at UC San Diego

• Math 109: Mathematical Reasoning, Fall 2026
• Math 109: Mathematical Reasoning, Winter 2027
• Math 142B: Advanced Calculus (Real Analysis II), Winter 2027
• Math 109: Mathematical Reasoning, spring 2027

Instructor at Berkeley

• Math 110: Abstract Linear Algebra
  [Course Website]

TA at Berkeley

• Math 143: Elementary Algebraic Geometry
• Math 135: Set Theory
• Math 113: Abstract Algebra
• Math 1B: Calculus
• Math 54: Linear Algebra and Differential Equations
• Math 74: Transition to Upper Division Mathematics

TA at Carnegie Mellon

I have been an undergraduate TA for the following courses.

• 21-127: Concepts of Mathematics
• 33-142: Physics II for Engineers

About

I grew up in Fresno, California. Outside of mathematics, I like playing board games, including Netrunner, and Magic: The Gathering. I listen to classical music, play clarinet, and also listen to Midwest emo (Spotify playlist). I enjoy audiobooks and composing orchestral arrangements of pop songs. I boulder and do Latin dance. I am learning Hungarian and would like to learn Mandarin.

Miscellaneous

Here are some other things I have made:

• Riddles
  [Link]
• Paintings
  [Link]

Rectangular toast generator, made by Atticus Cull, an undergraduate I mentored.

My Erdős number: 3