The SUMS lectures are a series of lectures organized by SUMS with the purpose of expanding undergraduate math students' knowledge. We will be getting professors, grad students to speak on a topic they find interesting. They will normally be held weekly on Wednesdays at 3:30, but check here for more information.
Upcoming lectures are listed below.
Past Lectures:
On a paper by Laplace by Niky Kamran
Date: Wednesday, November 24
Time: 2:00pm
Where: Burnside 1120
About:
In 1779, Laplace introduced an elementary (but ingenious) method for solving certain classes of partial differential equations. Laplace's approach was effectively a generalization of d'Alembert's famous method for solving the equation of a vibrating string. A geometric interpretation of Laplace'swork was given by Darboux in Volume II of his treatise on surface theory, published in 1896. It involves a beautiful transformation theory for surfaces, which has ramifications for problems of current research in differential geometry. We will give an elementary account of some of these results.
Lower bounds on quantum query complexity by Artem Kaznatcheev
Date: Tuesday, November 9th
Time: TBA
Place: TBA
About:
One of the outstanding problems in mathematics and theoretical computer science is to find lower bounds on the complexity of computational problems. However, it has proven difficult to make progress in fully general frameworks such as Turing-machines, circuits, or RAM models. Instead, we study more restricted and structured models of computation such as decision-tree or query models. In particular, the query model has been used to show concrete separations between quantum and classical computation. I will introduce the basics of quantum computing and the query model. If time permits I will also prove the spectral adversarial methods for lower bounds on quantum query complexity. The method provides an elegant and tight characterization of quantum query complexity. The talk will be mostly self-contained, no knowledge of quantum mechanics is required, but knowledge of linear algebra and appreciation of algorithms is welcome.
L-functions by Maksym Radziwill
Date: Tuesday,October 26th
Time: 3:00
Place: Burnside Room 1234
About:
I will give an very elementary introduction to the "theory" of L-functions.
Those are special functions that one attaches to sequences of integers
(like the primes). We apply methods from analysis (or calculus) to study them,
and deduce information about the sequence of interest.
The prime example is the so-called "Riemann zeta function". There is essentially
a one-to-one correspondence between the behavior of the sequence of prime numbers
and the location of the zeroes of the Riemann zeta function. This will be all
explained (it will be particularly clear if you took complex variables)
We will start with a proof of the infinitude of the primes (using L-functions).
You might like this proof because I will deduce that there are infinitely many primes,
from the irrationality of Pi^2!
Heekyoung Hahn
Date: Wednesday, October 20th
Time: 3:00
Place: Burnside Room 1234
About:
In this talk, we discuss the Selberg trace formula and its applications. No prior knowledge is required.
Sara Froehlich
Date: Wednesday, October 13th
Time: 3:30
Place: Burnside Room 1234
About:
If you have taken a first year analysis course, you undoubtedly saw the
Brouwer fixed point theorem in 1-dimension. For those unfamiliar with it,
we will review the proof of this theorem which only relies on knowledge of
the intermediate value theorem. We will then discuss several
generalizations of Brouwer's fixed point theorem, aiming to explore some
surprisingly wonderful applications of these more general fixed point
theorems.
Deal or No Deal: A Probabilistic Approach by Daphna Harel
Date: Wednesday, October 6th
Time: 3:30
About:
Ever seen the TV show Deal or No Deal? In this talk - we will analyze the basic probability theory behind the popular game show Deal or No Deal and discuss when a banker's offer is statistically "good". This talk is aimed at anyone - though a basic understanding of probability theory is helpful.