Math
I am a graduate student in mathematics at MIT, so I often think about math. The kinds of math I like best are
 visual: with drawing, pictures, or things to play around with;
 surprising: where different areas of math collide; and
 accessible: I can explain it to most anyone.
The specific area I research is called combinatorial, discrete, and convex geometry, which is all about patterns and structure of geometric objects. It checks all the boxes: I can explain the problems to other people (even if they aren't a mathematician), but the solutions are surprising and satisfying, often relying on connections to other fields of math, such as graph theory, probability, topology, and linear algebra. As you can see in the picture, I am occasionally a serious mathematician. (But not too often.)
Current projects

Clandestine families of balls
Given a family of sets in Euclidean space, we call a specific pair of sets in the family secretive if their intersection contains a point that is not contained in any other set in the family. (This point is, of course, the secret they share.) We call the family clandestine if every pair of sets in it is secretive. What is the maximum size of a clandestine family of balls in \(\mathbb{R}^d\)?
If \(d=2\), then any clandestine family of disks has at most 4 members. János Pach and I are investigating this and related questions for \(d≥3\). 
Hellytype theorems
Helly’s theorem is one of the most fundamental results in combinatorial convex geometry. Jiří Matoušek observed that “Helly’s theorem [has] inspired a whole industry of Hellytype theorems”, and I am one of many cogs in that industry. Right now, I’m thinking about quantitative and integer versions of Helly’s theorem.

Layer number of the integer grid
Given a set of points in Euclidean space, imagine removing the vertices of its convex hull, looking at what remains, removing the vertices of its convex hull, and repeating. Each step peels away a layer of the set; thus, the number of layers a set has—its layer number—is a measure of the depth of the set’s innermost points. My current work, with Gergely Ambrus, is on improving the current best bounds on the layer number of the grid \(\{1,2,…,n\}^d\).
Papers
My papers can be found in reversechronological order on the arXiv.
Discrete and convex geometry
 Variations on a theme of empty polytopes (with S. Arun), preprint (2024).
 Piercing intersecting convex sets (with I. Bárány, D. Pálvölgyi, D. Varga), preprint (2024).
 Explicit bounds for the layer number of the grid (with N. Varadarajan), preprint (2023).
 A mélange of diameter Hellytype theorems (with P. Soberón). SIAM Journal on Discrete Mathematics 35 (2021): 1615–1627. [arXiv]
 Discrete quantitative Hellytype theorems with boxes. Advances in Applied Mathematics 129 (2021): 102217. [arXiv]
Combinatorics
 Exponential multivalued forbidden configurations (with A. Sali). Discrete Mathematics & Theoretical Computer Science 23 (2021).
 An inverse problem for the collapsing sum. Australasian Journal of Combinatorics 79 (2021): 183–192.
 A combinatorial interpretation of Gaussian blur. Minnesota Journal of Undergraduate Mathematics 5 (2020).
Dynamical systems
 Dynamics and entropy of Sgraph shifts. Discrete and Continuous Dynamical Systems 42 (2022): 5637–5663. [arXiv]
Number theory
 An average of generalized Dedekind sums (with S. Gaston). Journal of Number Theory 212 (2020): 323–338. [arXiv]
Expository notes
 An introduction to graph limits. Onesemester course on dense graph limits at the advanced senior undergraduate level.
 Survey of enumerative combinatorics. Notes from a onesemester topics course taught by Alex Postnikov.
 Algebraic topology. Notes from a onesemester course.
 Rational choice theory. A quick tour through some aspects of the theories of social choice and games.
 Proof of G.E. Andrew's theorem that the number of vertices in a lattice polytope \(P\) in \(\mathbb{R}^d\) is at most \(O_d\big(\operatorname{Vol}(P)^{\frac{d1}{d+1}})\).