Past Events

A common theme in extremal combinatorics is when the random construction is close to optimal. In 1962, ErdH{o}s conjectured that the random $2$-edge-coloring minimizes the number of monochromatic copies of

The notable claim of quantum supremacy presented by Google's team in 2019 consists of demonstrating the ability of a quantum circuit to generate, albeit with considerable noise, bitstrings from a

Given a sequence of n independent tosses of a coin biased towards either heads or tails with probability 1/2 + β, the aim of the coin problem is to determine

The study of log-concave inequalities for combinatorial objects have seen much progress in recent years. One such progress is the solution to the strongest form of Mason's conjecture (independently by

Graph Crossing Number is a fundamental and extensively studied problem with wide ranging applications. In this problem, the goal is to draw an input graph G in the plane so

The Ramsey number r(G) of a graph G is the smallest integer n such that any 2-colouring of the edges of a clique on n vertices contains a monochromatic copy

Techniques for motion planning have advanced to address high-dimensional and complex environments. Understanding the approximations utilized in generating various robot configurations, as well as how much sampling is required to

Donald Knuth recently introduced the notion of a Baxter matrix, generalizing Baxter permutations. We show that for fixed number of rows, r, the number of Baxter matrices with r rows

Designing mechanisms to maximize revenue is a fundamental problem in mathematical economics and has various applications like online ad auctions and spectrum auctions. Unfortunately, optimal auctions for selling multiple items

Given a cooperative 2-player, 1-round game, we can consider its value - the maximum probability that the two players will win. The way the value changes when you repeat the

SAT-Hub aims to provide better location-aware services to traveling public, especially for underserved populations including those with visual impairment, Autism Spectrum Disorder (ASD), or simply navigation challenges, with minimal infrastructure

We examine complexity and versatility of five modulo 9 Kanade--Russell identities through their finite (aka polynomial) versions and images under the q -> 1/q reflection. This is a joint work

Crowdsourcing, peer grading, peer prediction, and surveys all require eliciting information from agents. Without a reward, agents may not participate, but providing rewards can distort incentives. For example, sophisticated agents

In this talk, I'm going to introduce polyhedral graphs and the problem estimating the diameter of a d-dim polyhedral graph with n facets. The problem is interesting in calculating the

Proving a 2009 conjecture of Itai Benjamini, we show: For any C, there is a > 0 such that for any simple random walk on an n-vertex graph G, the

In the 1870s, Lucas obtained a beautiful formula for binomial coefficients modulo p. Namely, Binomial[n, m] is congruent modulo p to the product of the binomial coefficients whose arguments are

Graphs are ubiquitous in science and engineering, and these graphs are often too big to store in RAM, may be distributed across many machines, and may be dynamic (meaning they

*Introductory 16-minute video (not required for the talk itself; if it does not load, try a different browser) https://idc-il.zoom.us/rec/share/DwDhgNJ5JOJt24ZgFOLUsD_ja5bIsoteWbjB3ujcb8pkIUjs--R7f43apwEBDyE.5n8Sff_mq6we4jsq Helly-type theorems and problems form a nice area of discrete geometry.

One well-known longstanding problem with Gosper’s algorithm is that its running time depends at least linearly on the dispersion of the rational certificate of the summand, and this last can

We revisit the well-studied problem of budget-feasible procurement, where a buyer with a strict budget constraint seeks to acquire services from a group of strategic providers (the sellers). During the