*Welcome to the official UMA website! The Undergraduate Mathematics Association is MIT's Math Club. Here, you can view past and upcoming events. Check out our Facebook page here. You can reach us at uma-request@mit.edu if you are interested in giving a talk or have any questions.*

**When and Where:** 5:30 pm on 12/04/19 in Room 491 at the Student Center

**Title:** End of Fall Term Dinner

**Description** Come celebtrate the end of the fall term with the MIT undergraduate math community!

**When and Where:** 5:30 pm on 11/13/19 in 4-270

**Title:** Recent breakthroughs in combinatorics

**Speaker:** Yufei Zhao

**Abstract** 2019 has been a great year for combinatorics. I will tell you about a few exciting results that came out in just the past few months: sensitivity conjecture, equiangular lines, sunflower conjecture, and the expectation threshold conjecture.

**When and Where:** 5:45 pm on 10/22/19 in 4-231

**Title:** Rational points on curves

**Speaker:** Wei Zhang

**Abstract:** What rational numbers can be the area of right triangles of rational sides? At what rational number does a polynomial f(x) take a square rational value? There are many of such Diophantine questions. We will discuss a few samples of existing results and some challenging open questions.

**When and Where:** 6:00 pm on 10/17/19 in 4-163

**Title:** Origami Flip Graph for Flat-Foldable Vertices

**Speaker:** Natasha Ter-Saakov

**Abstract:** Given a flat-foldable origami crease pattern C, we can describe how we fold it flat with a mountain-valley (MV) assignment, where each crease is described as bending convexly (mountain) or concavely (valley) when viewed from one side of the folding material. A MV assignment is called valid if it can be used to fold the crease pattern flat along all of its creases (i.e., it can be pressedin a book without crumpling or self-intersecting). We construct the *{origami flip graph*, OFG(C), from C as follows: the vertices are all valid MV assignments of C, and two vertices u and v are connected by an edge if and only if the MV assignment u can be turned into that of v by ``flipping" one face F of C (reversing the MV parity of the creases bordering F). In this talk, we examine origami flip graphs of single-vertex crease patterns.

**When and Where:** 5:30 pm on 9/26/19 in 4-270

**Title:** Manifolds and Modular Forms

**Speaker:** Sanath Devalapurkar

**Abstract:** We'll begin by talking about the Gauss-Bonnet theorem, and discuss how it expresses the integral of a geometric quantity on a surface as a purely topological one (and this topological quantity is in fact a number). Then, we'll discuss how one might attempt to generalize this sort of result to higher dimensions, as well as to manifolds with more structure. We'll find that there's an analogous result relating geometry to topology (a special case of the Atiyah-Singer index theorem), and argue that the resulting topological invariants are related to intricate structures showing up in number theory, such as modular forms. This story is a melting pot of multiple a priori distinct areas of math (differential geometry, algebraic topology, differential analysis, string theory, moonshine/representation theory, ...).

**When and Where:** 5:30 pm on 9/17/17 in 2-105

**Title:** MIT Math Breaker by Girl's Angle

**Description:** Girl's Angle presents a gift to the MIT Mathematics Department: a big collaberative puzzle for math majors!