CV
Basics
| Name | Swaroop S. Hegde |
| Research interests | Additive Combinatorics, Ramsey Theory, Probabilistic Methods in Combinatorics |
Education
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2021 - Present Athens, GA
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2015 - 2020 Bhubaneswar, India
Integrated M.Sc.
National Institute of Science Education and Research (NISER)
Mathematics
- Master's Thesis: Combinatorics and Representation Theory of Symmetric Groups
Work
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2021.08 - Present Instructor of Record
University of Georgia
Responsible for most aspects of the following courses including preparing course notes, delivering lectures, writing exams and quizzes, holding office hours and managing grades.
- Calculus I (Math 2250): Spring 2025, Fall 2024, Fall 2023, Spring 2023, Fall 2022
- PreCalculus (Math 1113): Fall 2026 (x2), Spring 2026 (x2), Fall 2025 (x2), Spring 2024 (x2), Spring 2022 (x2), Fall 2021
- Online Precalculus (Math 1113E): Summer 2024
Awards
- 2024.04
David Galewski Outstanding Graduate Teaching Award
Mathematics Department, University of Georgia
- 2024.03
Outstanding Teaching Assistant Award
Center for Teaching and Learning, University of Georgia
- 2018.09
Certificate of Merit
School of Mathematical Sciences, NISER
For outstanding performance in the Spring 2018 semester.
- 2015.08
INSPIRE Scholarship Award (2015-2020)
Department of Science and Technology, Govt. of India
Publications
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2026.09 A somewhat sure note on an un-Schur problem
S. Hegde, H. Kumar, Pratibha
arXiv preprint arXiv:2609.18474
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2026.08 Refined upper bounds on Schur-like numbers
S. Hegde, A. Lott, G. Petridis, N. R. Ponagandla
arXiv preprint arXiv:2608.03661
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2026.05 Extensions of the Furstenberg-Sárközy theorem via the arithmetic level-d inequality
C. F. E. Adajar, R. Agrawal, M. R. Choudhuri, C. Y. Chuah, S. Fan, S. Hegde, A. Lott, K. Nandakumar, and N. R. Ponagandla
arXiv preprint arXiv:2605.16216
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2025.10
Courses
| Selected Graduate Courses | |||||||||||||
| Entropy Methods in Combinatorics | |||||||||||||
| Ramsey Theory | |||||||||||||
| Additive Combinatorics I & II | |||||||||||||
| Probabilistic Methods in Combinatorics | |||||||||||||
| Ergodic Theory | |||||||||||||
| The Circle Method | |||||||||||||
| Equations with Prime Variables | |||||||||||||
| Algebraic Graph Theory | |||||||||||||
| Quiver Representations | |||||||||||||
| Commutative Algebra | |||||||||||||
| Lie Algebras | |||||||||||||
| Hopf Algebras | |||||||||||||
| Selected Reading Courses | ||||||
| Asymptotics of Ramsey Number R(4,t) (Oral Exam) | ||||||
| Kelley-Meka bound for Roth's theorem | ||||||
| Some recent improvements on Freiman's Theorem | ||||||
| Polynomial Methods in Combinatorics | ||||||
| Reflection Groups | ||||||
Conferences/workshops
- 2026.08
Graduate Workshop in Logic and Combinatorics
University of Illinois at Chicago
- 2026.06
International Conference on Graph Theory and its Applications (ICGTA 2026)
Presidency University, Bangalore, India
- 2026.06
Simons School and Workshop on Harmonic Analysis and applications to Ramsey theory
Rényi Institute, Budapest, Hungary
- 2026.05
Simons School and Workshop on Harmonic Analysis and Analytic Number Theory
Rényi Institute, Budapest, Hungary
- 2026.03
Graduate Student Combinatorics Conference
University of Illinois at Chicago
- 2025.07
PCMI 2025 Graduate Summer School on Extremal Combinatorics and Probabilistic Methods
PCMI, Park City, Utah
- 2025.06
Graduate Research Workshop in Combinatorics
Iowa State University, Ames, Iowa
- 2025.05
CanaDAM Conference 2025
Ottawa, Ontario, Canada
- 2025.05
Integers Conference 2025
University of Georgia, Athens, GA
- 2025.03
Algebraic and Analytic Methods in Combinatorics
SLMath, Berkeley, California
- 2025.02
Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural
SLMath, Berkeley, California
- 2024.06
Early-Career Conference in Combinatorics
University of Illinois Urbana-Champaign, IL
- 2024.05
33rd Cumberland Conference on Combinatorics, Graph Theory & Computing
Mississippi State University, MS
- 2023.06
Formalization of Mathematics
SLMath, Berkeley, California
- 2023.05
Integers Conference 2023
University of Georgia, Athens, GA
- 2017.06
ATM-Schools AIS on Representation Theory of Finite Groups
Chennai Mathematical Institute, Chennai, India
- 2017.06
Madhava Mathematics Camp
Indian Statistical Institute, Bangalore, India
- 2015.12
National Science Camp (VIJYOSHI)
Kolkata, India
Talks
- 2026.09
Generalized Schur Numbers
UGA Analysis Seminar
- 2026.03
An Inverse Result for Ruzsa's Inequality on Triple Sumsets
Graduate Student Combinatorics Conference, University of Illinois at Chicago
- 2025.10
An Inverse Result for Ruzsa's Inequality on Triple Sumsets
Discrete Math Seminar, Iowa State University (virtual)
- 2025.05
An Inverse Result for Ruzsa's Inequality on Triple Sumsets
CanaDAM Conference, Ottawa, Canada
- 2025.05
An Inverse Result for Ruzsa's Inequality on Triple Sumsets
Integers Conference, UGA
- 2024.03
Ramsey number R(4,k)
Oral Qualifying Exam Presentation, UGA
- 2023.10
AKS Algorithm for Primality Testing
Combinatorial Number Theory Reading Seminar, UGA
- 2023.10
A Polygon Problem
Graduate Student Seminar, UGA
- 2023.04
The RSK Correspondence
Graduate Student Seminar, UGA
- 2023.02
Almost Periods of Convolutions and Application to Roth's Theorem
Additive Combinatorics Reading Seminar, UGA
- 2022.11
Cores and Quotients of Integer Partitions
Graduate Student Seminar, UGA
- 2021.09
Rédei's Theorem and Szőnyi Method
Polynomial Methods Reading Seminar, UGA
- 2019.04
Roth's Theorem via Finite Fourier Analysis
Math Seminar, NISER
- 2018.04
Pebbling the Chessboard
NISER Open Day
- 2017.02
The Story of Dimension
MathematiX Club, NISER
- 2016.04
Clock Arithmetic
NISER Open Day (for high school students)
- 2015.11
Gödel's Incompleteness Theorems
MathematiX Club, NISER
Mentoring
- 2021.06 - Present
Directed Reading Program, UGA Math Department
Mentored UGA undergraduate students on various projects
- Yan Heng: Formalization of Mathematics in Lean, Spring 2026
- Benjamin Wang-Tie: Applications of Entropy in Combinatorics, Spring 2025
- Aakash Khanal: Mathematics of Card Shuffling, Summer 2021
Service
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2026.04 - 2026.04 -
2025.01 - 2025.05 -
2024.01 - 2024.05 Co-facilitator of the Precalculus community working group
Mathematics Department, University of Georgia
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2023.10 - 2024.10 Volunteer for High School Math Tournament
University of Georgia
Volunteered in Oct 2023 and Oct 2024.
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2023.08 - 2025.05 -
2022.08 - 2023.05