Department of Mathematics

Fine Hall

Princeton, NJ 08542

email: gk13(at)princeton(dot)edu

office: Fine Hall 904

I am currently a fifth year graduate student in Princeton University under the supervision of Peter Sarnak. I obtained my undergraduate degree from the National and Kapodistrian University of Athens.

I am broadly interested in the geometry of numbers, homogeneous dynamics and analytic number theory. A large part of my work is focused on understanding the spectra of polynomial differential operators acting on local geometries. I am also interested in applying tools from homogeneous dynamics to count integer or prime points on varieties.

*Bass Note Spectra of Binary Forms*

Submitted, 2024. (arXiv)*(with Katharine Woo) Prime Number Theorems for Polynomials from Homogeneous Dynamics*

Submitted, 2023 (arXiv)

Upcoming Talks:

- Princeton Number Theory Seminar- October 31 2024
- Online Seminar in Diophantine Approximation and Related Topics- November 21 2024
- GANT Algebra and Number Theory Seminar- December 5 2024
- Program at HUJI: Dynamics and Number Theory- December 26 2024

Recent Talks:

- Recent Trends in Homogeneous and Teichmüller Dynamics- September 26 2024
- Canadian Number Theory Association XVI (CNTA XVI)- June 11 2024
- Joint Columbia-CUNY-NYU Number Theory Seminar- May 9 2024.
- EKPA and SEMFE Analysis Seminar- April 22 2024.

Past Teaching:

- Fall 2024: Assistant in Instructorship (AI) for MAT 215 Single Variable Analysis
- Spring 2024: AI for MAT 201 Multivariable Calculus
- Fall 2023: AI for MAT 203 Advanced Vector Calculus
- Spring 2023: AI for MAT 204 Advanced Linear Algebra
- Fall 2022: AI for MAT 215 Single Variable Analysis
- Spring 2022: AI for MAT 202 Linear Algebra with Applications
- Fall 2021: AI for MAT 103 Calculus I

Undergraduate Research:

*(with S.Armeniakos and V.Nestoridis) Approximation on compact sets of functions and all derivatives*

Monatshefte für Mathematik 197 (2022) (arXiv)*(with K.Kioulafa and V.Nestoridis) Universal Taylor Series on products of planar domains*

Complex Analysis and its Synergies 7 (2021) (arXiv)*Partially Smooth Universal Taylor Series on products of simply connected domains*

Monatshefte für Mathematik 193 (2020) (arXiv)

Other Activities:

- Spring 2022: I was a mentor for Momentum 4 Ukraine Tutoring Program for Ukrainian refugee students.
- Spring 2022: I was a mentor for the Directed Reading Program.
- Fall 2021 and Spring 2022: I organized a preparatory learning seminar for the 2022-2023 IAS Special Year with Noah Kravitz and Katharine Woo.
- Fall 2020: I contributed 5 talks on Furstenberg's proof of Szemeredi's theorem in the Sarnak student seminar.