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Research Interest
Research Interest
I am interested in mathematical logic, specifically in model theory and continuous logic.
My Talks
My Talks
Borel definability of invariant local types for a continuous NIP formula - BLAST 2026 at Baylor University (2026 Spring)
Borel definability of invariant local types for a continuous NIP formula - BLAST 2026 at Baylor University (2026 Spring)
In this talk, we will work within continuous first-order logic, where formulas take truth values in the unit interval. Given an x-type p and a formula f(x,y), we consider the defining map from the y-type space to the unit interval, where the image of a y-type q is the truth value of f(p,q). The properties of such defining maps for both full and local types have been extensively investigated in classical first-order logic, particularly for countable languages and models. Hrushovski, Peterzil, and Pillay established Borel definability of finitely satisfiable types in NIP theories. Later, Hrushovski and Pillay proved strong Borel definability (constructibility) for invariant full types. Simon further studied this question for NIP formulas and invariant local types, and proved another version of Borel definability. In this work, we prove an analogous Borel definability result for continuous logic, following their ideas. Combining this result with the well-known paper of Bourgain, Fremlin, and Talagrand, we obtain a characterization of NIP in terms of Borel definability of approximately realized (finitely satisfiable in continuous logic) types and invariant types, and mention several functional-analytic corollaries.
NIP Formulas and Generic Sets in Pseudofinite Groups - The 25th Graduate Student Conference in Logic at Notre Dame (2025 Spring)
NIP Formulas and Generic Sets in Pseudofinite Groups - The 25th Graduate Student Conference in Logic at Notre Dame (2025 Spring)
We introduce the notions of NIP and VC-dimension, and explore their relationship. Using a theorem about VC-dimension, one can derive an analogous result in the setting of pseudofinite structures under the NIP assumption. As a corollary of this in the group context, we obtain a qualitative result for the genericity of formulas with positive pseudofinite counting measure.
The (Un)stable Formula Theorem - Louise Hay Logic Seminar at UIC (2024 Spring)
The (Un)stable Formula Theorem - Louise Hay Logic Seminar at UIC (2024 Spring)
Fix an L-theory T and a formula. We will define what it means for a formula to be stable and explore equivalent reformulations, following Shelah’s Unstable Formula Theorem. In particular, we will study the connections between the cardinality of type spaces, n-ladders, n-trees, and the definability of types.
Selected Presentations
Selected Presentations
Model Theory and Connes Embedding Problem (UIC 2024 Fall)
Model Theory and Connes Embedding Problem (UIC 2024 Fall)
A short exposition of the Connes Embedding Problem and Continuous Logic. Reformulation of CEP in terms of computability is outlined.
A Short Proof of Stable Graph Regularity Lemma (OSU 2024 Summer)
A Short Proof of Stable Graph Regularity Lemma (OSU 2024 Summer)
An alternative proof of the Stable Graph Regularity Lemma, originally proved by M. Malliaris and S. Shelah. The alternative proof is outlined by C. Terry and J. Wolf.
Zero-One Laws and Ehrenfeucht–Fraïssé Games (OSU 2024 Spring)
Zero-One Laws and Ehrenfeucht–Fraïssé Games (OSU 2024 Spring)
A short exposition of Chapter 10 of the book The Probabilistic Method written by N. Alon and J. Spencer.
Existence of Recursive Models of Decidable Theories (OSU 2023 Spring)
Existence of Recursive Models of Decidable Theories (OSU 2023 Spring)
On Vaught's proof that Henkin's construction in the proof of the Completeness Theorem is effective: for a recursive language L, any consistent decidable L-theory has a recursive model.
A Short Proof of Partition Theorem for Triples (METU 2021 Fall)
A Short Proof of Partition Theorem for Triples (METU 2021 Fall)
On the shorter proof provided by Albin J. Jones of one of the partition theorems of P. Erdős and R. Rado.
Conferences Attended
Conferences Attended
BLAST 2026 at Baylor University.
BLAST 2026 at Baylor University.
May 2026. Waco, Texas, US.
2025 North American Annual Meeting of the ASL at New Mexico State University.
2025 North American Annual Meeting of the ASL at New Mexico State University.
May 2025. Las Cruces, New Mexico, US.
Midwest Computability Seminar at The University of Chicago.
Midwest Computability Seminar at The University of Chicago.
November 2024. Chicago, Illinois, US.
The 2024 North American Annual Meeting of the ASL at The Iowa State University.
The 2024 North American Annual Meeting of the ASL at The Iowa State University.
May 2024. Ames, Iowa, US.
The 26th Graduate Student Conference in Logic at University of Illinois Chicago.
The 26th Graduate Student Conference in Logic at University of Illinois Chicago.
April 2026. Chicago, Illinois, US.
The 25th Graduate Student Conference in Logic at Notre Dame.
The 25th Graduate Student Conference in Logic at Notre Dame.
April 2025. Notre Dame, Indiana, US.
Summer School in Additive Combinatorics at Rényi Institute.
Summer School in Additive Combinatorics at Rényi Institute.
June 2024. Budapest, Hungary.
Midwest Model Theory Day at The University of Illinois Chicago.
Midwest Model Theory Day at The University of Illinois Chicago.
October 2022. Chicago, Illinois, US.
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