Silvia Ghinassi, a postdoc at the IAS, will give a talk aimed at undergraduates on the Analyst’s Traveling Salesman Theorem this

In analysis, we asked ourselves a similar question: “Given again a list of cities (possibly infinite, even uncountable, or better, a continuum!), when can our traveling salesman travel them all in finite (optimal, in some sense) time?”. Peter Jones in 1990 answered the question, proving the so-called “The Analyst’s Traveling Salesman Theorem”. We will discuss this theorem, its proof and related results (old and new).

Hope to see you there!

Sincerely,

Alice, co-advising chair ]]>

Tomorrow’s math colloquium will be featuring Professor Tristan Buckmaster, who will be presenting on convex integration and phenomenologies in turbulence).

Who? **Professor Tristan Buckmaster**

What? **Convex integration and phenomenologies in turbulence**

When? **Tuesday, November 5 at 4:30pm**

Where? **Fine 214**

Food? **Your choice of Bubble Tea and Tacos (which we will not bring, but if you brought yourself tacos you could have a Math Talk Taco Tuesday, which sounds really hard to pass on)**

Abstract: **In this talk, I will discuss a number of recent results concerning wild weak solutions of the incompressible Euler and Navier-Stokes equations. These results build on the groundbreaking works of De Lellis and Székelyhidi Jr., who extended Nash’s fundamental ideas on flexible isometric embeddings, into the realm of fluid dynamics. These techniques, which go under the umbrella name convex integration, have fundamental analogies with the phenomenological theories of hydrodynamic turbulence.**

We hope to see you there!

Your academic chairs, Nathan and Tristan

We will be featuring Dr. Yunqing Tang with a talk on elliptic curves. Here are some curves.

Who? **Dr. Yunqing Tang**

What? **Arithmetic of elliptic curves**

When? **Friday, October 18 at 5:00pm**

Where? **Fine Room 214**

Food? **Your choice of Bubble Tea**

Abstract: **Given an elliptic curve E over the ring of integers (in other words, consider the curve defined by y^2=x^3+Ax+B with A, B integers), we may ask what we can say about the mod p reduction of E. Elkies proved that there are infinitely many primes p such that E mod p are supersingular (equivalently, the above equation in x and y has exactly p solutions). I will give a very brief sketch of Elkies’s proof using the modular curve (the moduli space of elliptic curves) and also talk about how similar ideas can be used to prove other results, for instance, Habegger’s theorem, which asserts that there are only finitely many CM elliptic curves whose j-invariants are algebraic integers. If time permits, I will give some ideas on what to expect for higher dimensional generalizations.**

We hope to see you there!

Your academic chairs, Nathan and Tristan

We will be featuring Professor McConnell from the math department; topic of the talk TBA. Does Professor McConnell’s name sound familiar? He may or may not be the person who McConnell Hall is named after.

Who? **Professor Mark McConnell**

What? **An Algorithm for Hecke Operators**

When? **Wednesday, October 2 at 4:30**

Where? **Fine Room 214**

Food? **Your choice of BOBA and BYOS**

Abstract: A lattice is a discrete subgroup of R^n isomorphic to Z^n. In the plane, where n=2, the square lattice and the honeycomb are familiar examples. The space of all lattices can be studied via the *well-rounded retract* for SL_n, which is a complex glued together from topological cells. When n=2, the well-rounded retract is a tree with three edges meeting each vertex. Hecke operators act on the cohomology H^i of these spaces, and their eigenvalues are important in number theory. Previous algorithms to compute Hecke operators have worked for all n, but only in a narrow range of i depending on n. The talk will present a 2016 algorithm of Robert MacPherson and myself that works for SL_n for all n and all i. The talk will not assume any detailed background in topology or cohomology.

If you have any further questions, please let us know!

We hope to see you there!

Your academic chairs, Nathan and Tristan

A summary of the film: Lecturer Solomon Lefschetz uses many geometric examples to describe how his magic number applies in determining whether a surface has the fixed point property. Includes an informal chat in which Professors Leon Cohen, Shizuo Kakutani, and A.W. Tucker discuss the history of topology and mathematics with Professor Lefschetz.

]]>Description: For centuries, mathematicians have studied the integer solutions to equations like x^2+y2=z^2, x^2-Dy^2=1, x^n-y^m=1, and we still seek a general theory of such Diophantine equations. We will discuss how this question is deeply tied with the geometry of such equations, and how it naturally leads to the study of elliptic curves. No prior knowledge will be assumed.

RSVP here for pizza!

Best of luck with deans date/finals!

~Alec

Here’s the information for the first colloquium, which is happening tomorrow!

Who? **Professor Richard Ehrenborg**

What? **A theorem by Baxter**

When? **Wednesday, May 1st at 4:30pm**

Where? **Fine Hall 214**

Food? **Your choice of Large-Sized Boba (we’re going all out this week) or Regular-Sized Boba Fett**

Abstract: **We discuss a theorem by Baxter from 1966 on planar graphs.**

By reformulating the theorem we make an incursion into topology

and prove analogous results in higher dimensions. A connection

with Sperner’s Lemma is also highlighted.

Joint work with Gábor Hetyei.

By reformulating the theorem we make an incursion into topology

and prove analogous results in higher dimensions. A connection

with Sperner’s Lemma is also highlighted.

Joint work with Gábor Hetyei.

There will be large-sized boba.

Now let’s talk about the second colloquium, which is happening on Friday.

Who?

What? **Analyzing Optimization in Deep Learning via Trajectories**

When? **Friday, May 3rd at 4:30pm**

Where? **Fine Hall 214**

Food? **Your choice of Large-Sized Boba (we weren’t kidding above about going all out this week) or Post-Sarlacc Pit Boba Fett**

Abstract: **The prominent approach for analyzing optimization in deep learning is based on the geometry of loss landscapes. While this approach has led to successful treatments of shallow (two layer) networks, it suffers from inherent limitations when facing deep (three or more layer) models. In this talk I will argue that a more refined perspective is in order, one that accounts for the specific trajectories taken by the optimizer. I will then demonstrate a manifestation of the latter approach, by analyzing the trajectories of gradient descent over arbitrarily deep linear neural networks. We will derive what is, to the best of my knowledge, the most general guarantee to date for efficient convergence to global minimum of a gradient-based algorithm training a deep network. Moreover, in stark contrast to conventional wisdom, we will see that sometimes, gradient descent can train a deep linear network faster than a classic linear model. In other words, depth can accelerate optimization, even without any gain in expressiveness, and despite introducing non-convexity to a formerly convex problem.**

We hope to see you there!

Your academic chairs,

Nathan and Tristan

PS: For those of you who watched Endgame already, I was traumatized when they killed Batman.

PSS: For those of you who are all caught up on Game of Thrones, it was really sad to see Gandalf die.

If you need a guest swipe, please let me know. Hope to see you there!

Your math club advising chairs,

Alice and Gary

]]>technically this is the view from the top of the burj khalifa, but close enough

Do you like **free food?**

did any of you try the vodka penne they had in jadwin for the debate competition a few weeks ago? soooooooo goooooood

Then please click here to RSVP to the **Math Club’s end-of-year banquet!** It will be on **Wednesday, May 8th** from **6:00 to 9:00pm** in the **Fine Hall professor’s lounge**, and it will be a great way to celebrate and reflect upon this year. We need your responses by **this Friday** so we know how much food (caterer TBD) to order!

this is me preemptively stopping all of you people who i know are gonna criticize my use of the word “please” in that way

We hope to see (exactly the people who RSVP’d) there! Your Math Club social chairs,

Alec Leng and Matt Yua

]]>