I am a postdoc of Mikołaj Frączyk at the Dioscuri Center "Random Walks in Geometry and Topology" at the Jagiellonian University in Krakow, Poland.

I completed my Ph.D. in 2026 at the math department at UW-Madison under the supervision of Andrew Zimmer and Sebastian Hurtado-Salazar. Prior to studying in Madison, I was an undergrad at the University of Chicago. 

Here is a copy of my CV.

Note: I believe artificial intelligence (AI) is very harmful to mathematics, the mathematical community, and humanity as a whole. Consequently, I do not and will not use AI in any form in my mathematical works, nor in my personal life. This beautiful blog post of Hugo Duminil-Copin describes many of the concerns I have with the use of artificial intelligence in mathematics. I also wholeheartedly agree with this wonderful blog post of Jonny Evans.

"Everything had changed suddenly -- the tone, the moral climate; you didn't know what to think, whom to listen to. As if all your life you had been led by the hand like a small child and suddenly you were on your own, you had to learn to walk by yourself... At such a time you felt the need of committing yourself to something absolute -- life or truth or beauty -- of being ruled by it in place of the man-made rules that had been discarded. You needed to surrender to some such ultimate purpose more fully, more unreservedly than you had ever done in the old familiar, peaceful days, in the old life that was now abolished and gone for good." -- Boris Pasternak, Doctor Zhivago

AI companies and other actors have engaged, and continue to engage, in standard bullying behavior by abusing and attempting to terrorize and frighten the mathematical community for their own benefit. I refuse to allow this to influence the manner in which I study and work on mathematics, which is the activity I love the most in this world. Regardless of what they say, it is clear to me who these people are from their works:

"Beware of false prophets, who come to you in sheep's clothing, but inwardly they are ravenous wolves. You will know them by their fruits. Do men gather grapes from thornbushes or figs from thistles? Even so, every good tree bears good fruit, but a bad tree bears bad fruit. A good tree cannot bear bad fruit, nor can a bad tree bear good fruit... Therefore by their fruits you will know them.'' -- Matthew 7:15-20.

Papers:

5. Growth gaps and generating sets (joint with Gal Yehuda)

Submitted, 11 pages.

4. Zariski density of discrete subgroups via critical exponents and unitary representations 

Submitted, 15 pages.   

3. Rigidity of proper holomorphic maps between balls with Hölder boundary regularity (joint with Kyle Huang, Jinwoo Park, Jaan Amla Srimurthy, Andrew Zimmer, and Rou Wen)

Journal of the London Mathematical Society, to appear, 20 pages. MXM project!

2. Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups

Submitted, 39 pages.

1. Free semigroups of large critical exponent

Journal of Topology, Vol. 19 (2026), no. 3, Paper No. e70087, (47 pages).

Mathematical Interests:

My mathematical interests are in geometry and dynamics, particularly discrete subgroups of higher rank Lie groups. Recently, I have been especially interested in understanding asymptotic properties of discrete subgroups of Lie groups and the representation theory of semisimple Lie groups.

Other:

My thesis (essentially a combination of papers (1) and (2) above).