sueda.github.io/research.html at main · suedasenturk/sueda.github.io · GitHub

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<!DOCTYPE html>
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<title>Research – Sueda Senturk Avci</title>
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  <a href="index.html">Home</a>
  <a class="active" href="research.html">Research</a>
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<header>
  <h1>Research</h1>
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<section>

<p>
I currently work on
 modular forms, cusp forms, twisting, the
Rankin–Selberg method, the analytic computation of the constant term of non-holomorphic Eisenstein series,
local fields, adeles, p-adic integration, and the special functions that arise in explicit computations.
 </p>
 <p>
I also
study the computation of all Fourier coefficients and encountered the Whittaker function in the big Bruhat
cell. To understand this construction more thoroughly, I studied the relevant representation-theoretic background, including degenerate principal series and the Schrödinger model of the Weil representation, following
Yang’s CM Number Fields and Modular Forms and Kudla–Yang’s Eisenstein Series for SL(2), which I am
currently reading in depth. These studies have shaped my current project on generalizing Whittaker function
constructions.

</p>

<p>
 In Algebraic Topology I studied free resolutions using augmented chain complexes,
which gave me helpful intuition for homological tools that appear in the study of arithmetic groups.
</p>

<p>
In Algebraic Geometry I explored the connection between the j-invariant and ring class fields, following portions of Gross–Zagier
and Cox.
</p>

 <p>
 In Matrix Analysis I studied the correspondence between ideal classes and similarity classes of matrices
through the Latimer–MacDuffee theorem, discovering a surprising link to class numbers.
 </p>

 <p>
In Summer 2023, I completed a Directed Reading Program on the Dirichlet Class Number Formula under the guidance of Gaurish Korpal.
</p>

<p>
   In Spring 2023, I worked on a project focused on application of category theory, under the supervision of Prof. Olcay Coskun.
In this project we studied the Prof. Tom Leinster's paper called Entropy and Diversity: The Axiomatic Approach.
Here I learned about how to grasp physical concepts like entropy in pure algebraic ways.
   </p>


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