# Algebraic and Geometric Structures in Extremal Combinatorics

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · Carnegie Mellon University (PA) · $180,000

## Abstract

The aim of this project is to better understand mathematical structures that are 1) discrete, and 2) are of geometric and algebraic nature. The examples of discrete structures include networks, matrices and arrangements of convex sets. There are a number of instances where the optimal discrete objects necessarily possess non-trivial algebro-geometric properties. This project is devoted to understanding this phenomenon. Students will be mentored as part of the project.

The specific problems include algebraic and geometric questions related to the Turan problems and combinatorial questions in finite geometry. 
Particular attention will be devoted to algebraic constructions, especially in mixed characteristic. The potential impacts include a new method for testing conjectures in discrete geometry and better locally decodable codes.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

## Key facts

- **NSF award ID:** 2452120
- **Awardee organization:** Carnegie Mellon University (PA)
- **SAM.gov UEI:** U3NKNFLNQ613
- **PI:** Konstantin Tikhomirov
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** —
- **Estimated total:** $180,000
- **Funds obligated:** $180,000
- **Transaction type:** Standard Grant
- **Period:** 08/15/2025 → 07/31/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2452120

## Citation

> US National Science Foundation, Award 2452120, Algebraic and Geometric Structures in Extremal Combinatorics. Retrieved via AI Analytics 2026-06-06 from https://api.ai-analytics.org/grant/nsf/2452120. Licensed CC0.

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