The Graduate Student Seminar (GSS) is a weekly seminar in the Brandeis Mathematics Department run by the GSS organizers: Neha Goregaokar and John Michael Figueroa, the Graduate Department Representatives.
GSS is a great way to learn how to give research talks
before you've learned enough to enlighten other mathematicians with your amazing research and
in a low-pressure environment.
It's difficult to overstate the importance of communicating your research effectively. You can speak about whatever you're reading now, your research, or something you think all math grad students should know. So, join us and learn the skill many mathematicians never learn.
The seminar is by grad students and for grad students only! Faculty are not allowed to come.
You can view some previous semesters' schedules by using the navigation at the top of the page.
Spring 2026
January 29 -- John Michael Figueroa
Title: The Rado graph and other Fraïssé limits
Abstract: Suppose we construct an infinite random graph --- ie, make a vertex for each natural number, then choose edges randomly. What does the resulting probability distribution over the space of graphs look like? What properties does an infinite random graph have, and how do they relate to finite random graphs? We'll take a look at the model theory of the infinite random graph (including a surprising connection to non-standard models of set theory!). We'll see that it's a special case of the notion of a Fraïssé limit, the theory of which we'll explore.
February 5 -- Neha Goregaokar
Title: Equitable Coloring of Random Graphs
Abstract: This talk will be based on the paper Equitable colorings of random graphs by Michael Krivelevich and Balázs Patkós. The talk will cover equitable chromatic numbers and thresholds as well as some results about their asymptotic behavior.
February 12 -- Sarah Dennis
Title: A fast solver for the Reynolds equation
Abstract: Lubrication theory leverages the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate an approximation to the 2D incompressible Navier-Stokes equations. The resulting 1D Reynolds equation is an elliptic differential equation describing the fluid pressure. When the height (or thickness) of the fluid is linear, the Reynolds equation has an exact solution. Through approximating the height of the fluid as piecewise linear and coupling the exact solutions on each sub-interval, we formulate a solution which is exact in the case of piecewise linear heights and is a second order approximation in the case of arbitrary heights. This method of solution can be obtained in linear time, proportional to the number of piecewise components. In the talk I will go over the background for lubrication theory and deriving the Reynolds equation, then I will present the aforementioned method of solution. If there is time, we will look at some examples and compare the solution from lubrication theory with the solution from the Stokes equations.
February 26 -- Tudor Popescu
Title: The sum-product conjecture
Abstract: In this talk, we will discuss different bounds for one of the most interesting additive combinatorics conjectures. While the proofs are advanced and deep, they don't require any background, and we will see how probability, incidence geometry, combinatorics, and number theory combine marvelously.
March 5 -- TBD
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March 12 -- TBD
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March 19 -- TBD
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March 26 -- TBD
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April 16 -- TBD
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April 23 -- TBD
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April 28 -- TBD
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