This is an informal reading seminar on combinatorics run by myself and Bhargav Narayanan. It differs from GCS in that our focus here is to discuss papers, and some may be more advanced than what is typically done at GCS. There is also a requirement that each participant present during the semester. However, there are no formal prerequisites; anyone interested is welcome to join. Email me if you want to be on the mailing list.

## Upcoming Seminars

This semester, our reading seminar will be on discrete geometry. Our main reference is Matousek's Lectures on Discrete Geometry. We will meet in Hill 701 from 5-6:30pm on Mondays.

- December 12, Quentin Dubroff
- December 5, Corrine Yap
- November 28, Dennis Hou
- November 21, Maxwell Aires
- November 14, Forrest Thurman, followed by problem session
- November 7, Zeyu Zheng
- October 31, Vikrant Ashvinkumar (Section 5.6, 6.1)
- October 24, Minhao Bai (Section 5.4-5.5)
- October 17, Rashmika Goswami (Section 5.3)
- October 10, Caleb Fong, followed by problem session with Sam Spiro (Sections 5.1-5.2)
- October 3, Charles Kenney (Section 2.1)
- September 26, Natasha Ter-Saakov (Sections 1.1-1.4)

## Past Seminars

For spring 2022, the reading seminar was on percolation. We used lecture notes from
Perla Sousi and
Hugo Duminil-Copin.

- May 2, Dennis Hou (Sousi: Section 1.11)
- April 25, problem session with Ben Gunby (D-C: Exercise 25)
- April 18, Forrest Thurman (Schramm: Scaling limits of loop-erased random walks and uniform spanning trees)
- April 11, Quentin Dubroff (Sousi: Section 2.4-2.5)
- April 4, Kayla Gibson (Sousi: Section 1.9-1.10)
- March 28, problem session with Ben Gunby (D-C: Exercises 14, 19, 20)
- March 21, Minhao Bai (Sousi: Section 1.7-1.8, pg. 19-24)
- March 7, Charles Kenney (Sousi: Section 1.6, pg. 16-19)
- February 28, Natasha Ter-Saakov (Sousi: Theorem 1.25 - Corollary 1.32, pg. 12-16)
- February 21, problem session with Ben Gunby (Sousi: Example Sheet 1, Problems 8, 9; D-C: Exercise 7)
- February 14, Rashmika Goswami (Sousi: Theorem 1.14 - Defn 1.24, pg. 6-11)
- February 7, problem session with Ben Gunby (Sousi: Example Sheet 1, Problems 1, 2; D-C: Exercises 2, 4)
- January 31, Corrine Yap (Sousi notes: beginning through Lemma 1.13, pg. 6)

- December 1, Natasha Ter-Saakov. The K^(ℵ_0) Game: Vertex Colouring (Bowler, Emde, & Gut).
- November 17, Corrine Yap. On the independent set sequence of a tree (Basit, Galvin).
- October 27, Shivam Nadimpalli. On Monotonicity Testing and Boolean Isoperimetric-type Theorems (Khot, Minzer, & Safra).
- October 20, Charles Kenney. Asymptotics for Shamir's Problem (Kahn).
- September 29, Quentin Dubroff. Proof of the Van den Berg-Kesten Conjecture (Reimer).

- April 15, Corrine Yap. On a problem of Spencer (Shearer) and more recent connections between the Lovasz Local Lemma and cluster expansion.
- March 25, Quentin Dubroff. Linear Cover Time is Exponentially Unlikely (Benjamini, Gurel-Gurevich, Morris).
- February 18 and 23, Shivam Nadimpalli, How much are increasing sets positively correlated? (Talagrand).
- February 4, 2021 Corrine Yap, Rainbow Turan Problem for Even Cycles (Das, Lee, & Sudakov).

- December 4, Rashmika Goswami, selections from Independent sets, matchings, and occupancy fractions (Davies, Jenssen, Perkins, Roberts)
- Monday, November 23, Quentin Dubroff, selections from Isoperimetry, logarithmic Sobolev inequalities on the discrete cube, and Margulis' graph connectivity theorem (Talagrand).
- Monday, November 9, Charles Kenney, Sphere coverings of the hypercube with incomparable centers (Füredi, Kahn, & Kleitman).
- October 16, Keith Frankston, Lower bounds for multicolor Ramsey numbers (Conlon & Ferber).
- October 2, Corrine Yap, selections from Irreducible polynomials of bounded height (Bary-Soroker & Kozma).
- August 28, Corrine Yap, Rota's Basis Conjecture holds asymptotically (Pokrovskiy).

- August 10, Jinyoung Park, Tuza's Conjecture for random graphs (Kahn & Park).
- July 24, Jinyoung Park, Random cliques in random graphs (Riordan).
- July 10, Corrine Yap, Nearly-linear monotone paths in edge-ordered graphs (Bucic, Kwan, Pokrovskiy, Sudakov, Tran, & Wagner)
- June 19, 26, Quentin Dubroff, The plank problem for symmetric bodies (Ball).
- June 9, Aditya Potukuchi, An upper bound on the number of Steiner triple systems (Linial & Luria).
- May 5, Quentin Dubroff, Tomaszewski's problem on randomly signed sums (Boppana & Holzman).
- April 28, Corrine Yap, Zero Trees Theorem (Schrijver & Seymour).
- April 14,
**3PM**: Aditya Potukuchi, Concentration on the boolean hypercube (Eldan & Gross). - March 3: Yonah Biers-Ariel, Communication is bounded by root of rank (Lovett).
- February 25: Quentin Dubroff, On sets of n points in general position that determine lines that can be pierced by n points (Keller & Pinchasi).
- February 4, 2020
**3PM**: Corrine Yap, Halfway to Rota's Basis Conjecture (Bucic, Kwan, Pokrovskiy, & Sudakov).