ABACUS Graduate Combinatorics Seminar

The purpose of this seminar is for graduate students in combinatorics at UCSD

  1. To become more familiar with recent and important results in combinatorics.
  2. To get practice at giving presentations.
  3. To build and foster a community amongst the combinatorics students at UCSD.
The seminar is organized by Jason O'Neill, Nick Sieger, Sam Spiro, and Emily Zhu; with additional support from the postdocs Gwen McKinley and Ruth Luo. Topics range from graph theory, to probabilistic methods, to algebraic combinatorics; and is largely determined by the interests of those who attend.

Our meetings for Winter 2021 will take place 3:00pm PST on Tuesdays, and at least to start we'll be giving talks themed around hypergraph containers based off of Balogh's notes. Directly after the talk we will have a social hour (DiscreTea) over Zoom. Below is the current schedule for speakers.

Date Speaker Title
Winter 2022
1/11/22 Melissa Fuentes The Extremality of 2-partite Turan Graphs with Respect to the Number of Colorings.
1/18/22 Nicholas Sieger On the open problem "Count the ways to add a K-4".
1/25/22 Nadia Lafrenière The spectrum of the random-to-below Markov chain.
2/1/22 Sam Spiro The Rational Exponent Conjecture.
2/8/22 Youngho Yoo Approximating TSP walks in subcubic graphs.
2/15/22 Sam Mattheus Polar spaces in extremal combinatorics.
2/22/22 Sidhanth Mohanty Testing thresholds for high-dimensional sparse random geometric graphs.
3/1/22 Alp Muyesser Rainbow spanning structures.
3/8/22 Calum MacRury Adaptive Strategies for Sparse Graphs in the Semi-random Graph Process.
Fall 2021
10/5/21 Jason O'Neill Towards supersaturation for oddtown and eventown.
10/12/21 Sam Spiro Slow Fibonacci Walks.
10/19/21 Grace McCourt On sizes of 1-cross intersecting set pair systems.
11/2/21 Kat Perry Rainbow Spanning Trees in Edge-Colored Complete Graphs.
11/9/21 Gabriel Elvin Fourier-analytic Methods.
11/16/21 Adam Wagner Constructions in combinatorics via neural networks.
11/23/21 N/A
11/30/21 Jane Tan Generalisations of a light switch problem.
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Spring 2021
3/30/21 Connor Mattes Flag Algebras and an application: C_5 is almost a fractalizer.
4/6/21 Gabriel Elvin Avoiding Monochromatic Structure.
4/13/21 N/A
4/20/21 Benjamin Gunby Upper Tails of Subgraph Counts in Sparse Regular Graphs.
4/27/21 Kyle Murphy Maximizing five cycles in K_{r+1}-free graphs.
5/4/21 Sean English Lower Bounds on Generalized Ramsey Numbers via Color Energy.
5/11/21 Adam Volk Graph Saturation and Counting Stars.
5/18/21 Jonathan Tidor The Joints Problem.
5/25/21 Jason O'Neill Intersection Saturated set systems.
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Winter 2021: Hypergraph Containers
1/5/21 Sam Spiro An Introduction to Hypergraph Containers.
1/12/21 Jason O'Neill A Random Variant of Sperner's Theorem.
1/19/21 Ruth Luo The Number of Maximal Triangle-free Graphs.
1/26/21 Nicholas Sieger The Number of Maximal Sum-Free Sets.
2/2/21 Jiaxi Nie Turan's Theorem in Random Graphs.
2/9/21 Sam Spiro Cycle-Free Subgraphs of Random Hypergraphs.
2/16/21 Everyone Organizational Meeting.
2/23/21 Everyone Open Problem Session I.
3/2/21 Everyone Open Problem Session II.
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Fall 2020
9/29/20 Gwen McKinley Counting integer partitions with the method of maximum entropy.
10/6/20 Sam Spiro Relative Turan Numbers of Hypergraphs.
10/13/20 N/A
10/20/20 Nicholas Sieger A Quick and Dirty Introduction to Higher Order Fourier Analysis
10/27/20 Chieu-Minh Tran Point-box incidences and logarithmic density of semilinear graphs
11/3/20 Sam Spiro Card Guessing with Partial Feedback
11/10/20 Kate Lorenzen Cospectral constructions for several graph matrices using cousin vertices
11/17/20 Xiaoyu He Two Universality Problems
11/24/20 N/A
12/01/20 Jason O'Neill An introduction to extremal problems on convex geometric hypergraphs
12/08/20 Emily Zhu On the Erdos-Hajnal Hypergraph Ramsey Problem
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Winter 2020: Spectral Graph Theory
1/10/20 Sam Spiro Introduction to Spectral Graph Theory and the Adjacency Matrix.
1/17/20 Jason O'Neill The Laplacian Matrix.
1/24/20 San Spiro The Normalized Laplacian Matrix.
2/7/20 Andres Rodriguez Towards a Theoretical Foundation for Laplacian-Based Manifold Methods.
2/14/20 Daniël Kroes Strongly Regular Graphs.
2/21/20 Jiaxi Nie (n,d,lambda)-graphs and Ramsey Numbers.
2/28/20 Nicholas Sieger Interlacing Families and Ramanujan Graphs I.
3/6/20 Nicholas Sieger Interlacing Families and Ramanujan Graphs II.
3/13/20 Max Hopkins High Dimensional Expanders.
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Fall 2019: Linear Algebra Methods
10/4/19 Daniël Kroes Oddtown, Eventown, and Frankl-Wilson.
10/11/19 Emily Zhu The Graham-Pollak Theorem.
10/18/19 Jason O'Neill Multilinear Polynomials.
10/25/19 Sam Spiro The Tensor Product Method and Exterior Algebras.
11/1/19 Jacob Naranjo Inclusion Matrices for Extremal Problems.
11/15/19 Jason O'Neill q-analogs for the Ray-Cahudhuri-Wilson Theorem.
11/22/19 Jiaxi Nie Slice Rank and the Capset Problem.
12/6/19 Nicholas Sieger Interlacing and the Sensitivity Conjecture.
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2018-2019 Schedule
6/17/19 Everyone Brainstorming Session.
5/24/19 Daniël Kroes Sums of Permutations.
4/26/19 Jason O'Neill Vinogradov's Three Prime Theorem.
4/12/19 Sam Spiro Roth's Theorem.
3/15/19 Renee Mirka The Rank Aggregation Problem.
3/1/19 Sam Spiro The Rodl Nibble.
2/15/19 Daniël Kroes Matroids and Their Applications.
2/1/19 Jason O'Neill The Kruskal-Katona Theorem.
1/19/19 Mozhgan Mirzaei The History of Extremal Problems for Cycles in Graphs.
11/30/18 Andres Rodriguez Hopf Monoids in Set Species.
11/16/18 Nick Sieger The Differential Equations Method and Ramsey Lower Bounds.
11/2/18 Thomas Grubb "Algebraic Combinatorial Geometry" by Terrance Tao.
10/19/18 Jason O'Neill Simple Random Walks in Dimensions 2 and 3.
10/5/18 Sam Spiro "On Random Graphs" by Paul Erdos and Alfred Renyi.