Fall 2022 – Summer 2023 – Abstracts


 

Wednesday, December 7, 2022. Mathematics Colloquium.

Dr. Brandon Hanson, University of Maine Mathematics.
“The unreasonable effectiveness of polynomials in the mathematical sciences”
3:15 – 4:15 pm, Room 101, Neville Hall (with refreshments at 3:00 pm)

Abstract:

Polynomials are ubiquitous objects in math, and provide a fantastic playground for testing hypotheses and formulating conjectures. They are the nicest functions we know of and have all sorts of regularity properties coming from different mathematical perspectives — analysis, geometry, algebra, number theory, combinatorics, etc. These regularity properties make polynomials a fantastic device for tackling problems which at first glance have nothing at all to do with polynomials — an approach sometimes called the polynomial method. In this, sure to be fantastic talk, I will discuss about the origins of the polynomial method and sketch how it is used to solve a number of interesting questions in various disciplines.


 

Friday, December 2, 2022. Graduate Seminar.

Crockett Lalor, University of Maine Mathematics MA student (advisor: Neel Patel).
“Why are all these cars parked on 495? Or, on the origin of road rage”
3:00 – 3:50 pm, 104 Jenness Hall

Abstract: In this talk, we’ll delve into the mysterious behavior of people in cars driving down the road. Why are they doing that strange thing? What is wrong with all these people? Through the power of partial differential equations we will find order in chaos, make sense of nonsense, understand the incomprehensible. By squinting our eyes, we change the discrete into the continuous and study the density of traffic in several situations familiar to the everyday motorist.


 

Wednesday, November 30, 2022. Mathematics Colloquium.

Dr. Tim Browning, IST Austria.
“Polynomials over ℤ and ℚ: counting and freeness”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall (with refreshments at 3:00 pm)

Abstract:

Humans have been thinking about polynomial equations over the integers, or over the rational numbers, for many years. Despite this, their secrets are tightly locked up and it is hard to know what to expect, even in simple looking cases. In this talk I’ll discuss recent efforts to understand the frequency of integer solutions to cubic polynomials, before turning to the much more evolved picture over the rational numbers.

About the speaker:

Professor Browning is a number theorist at the Institute of Science and Technology, Austria. He studies the integers using a mixture of analytic, geometric, and algebraic methods. He has been featured in several Numberphile videos:

 


Wednesday, November 16, 2022. Mathematics Colloquium.

Dr. Aden Forrow, University of Maine Mathematics.
“An Introduction to Likelihood-free Inference”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall (with refreshments at 3:00 pm)

Abstract:

A key challenge in modern statistical inference is developing algorithms to handle increasingly complex scientific data. For models in contexts from cosmology to psychology and neuroscience, standard analytical tools hit unsurmountable computational obstacles. Over the past two decades, a wide range of algorithms have been proposed for learning parameters of these models in computationally feasible ways, often under the heading of approximate Bayesian computation or likelihood-free inference. In this talk, I will present the core likelihood-free inference problem, building up by way of traditional maximum likelihood estimation and likelihood-based Bayesian inference with Markov chain Monte Carlo. We will investigate the surprisingly challenging question of determining how well a likelihood-free algorithm performs, finding at the end that appropriately evaluating performance can yield significant gains in computational efficiency.

 


Wednesday, November 9, 2022. Mathematics Colloquium.

Dr. Benjamin Weiss, Unum.
“Valuing Insurance Companies or How I learned to Stop Worrying and Love Quartic Splines”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall (with refreshments at 3:00 pm)

Abstract:

A recent change in accounting law has added a lot of new work for insurance companies to value their assets and liabilities for SEC reporting. We’ll give an introduction to financial valuations, and a brief history of the laws. This will lead us to needing to connect dots nicely (using linear algebra, and numerically stable algorithms). I expect interested undergraduates who have taken linear algebra would be able to follow the talk; I expect most faculty to know all the math, but be surprised at some of the history and applications.

Dr. Weiss works on the actuarial team at Unum, the country’s leading employer benefits insurer, in Portland. Unum employs many UMaine alumni (math majors, business majors, and many others too!). He would be happy to speak with students before and after the talk about employment opportunities.

 


Monday, November 7, 2022. Algebra Seminar.

Victor Carmona, University of Seville.
“Stabilization of algebras and functor calculus”
3:00 – 3:50 pm, 102 Jenness Hall

Abstract: From basic algebraic geometry, we know that infinitesimal neighborhoods and tangential data are controlled by nilpotent rings. In this talk, we will explain how this phenomenon is pretty general by explaining that it works for operadic algebras. Also, we will discuss what is the connection with Goodwillie calculus of functors.

 


Wednesday, October 26, 2022. Mathematics Colloquium.

Elena Salguero, University of Seville, Spain.
“The Dynamics of a Stokes Flow”
3:15 – 4:15 pm, Hill Auditorium, Barrows Hall (with refreshments at 3:00 pm)

Abstract:

The Navier-Stokes equations are partial differential equations describing the dynamics of a viscous fluid. They have proved to be very useful for their accuracy in modeling a large number of scientific phenomena: ocean currents, motion of stars, blood flow, etc. Their mathematical analysis is also of great importance, as the behavior of smooth solutions in three dimensions is still unknown. This question constitutes one of the seven most important open problems in mathematics. Despite the complexity of NS equations, we can study a wide range of related problems making certain assumptions over the flow. In particular, we will discuss the dynamics of two viscous fluids whose particles have negligible acceleration compared to viscous forces: the so-called Stokes or creeping flow regime.

 


Monday, October 17, 2022. Number Theory Seminar.

Petar Bakic, University of Utah.
“Theta correspondence and Arthur packets: the Adams conjecture”
3:00 – 3:50 pm, 102 Jenness Hall

Abstract: In his 1989 paper, Adams conjectured that the theta correspondence should exhibit functorial behavior with respect to Arthur packets. The conjecture is known to be true when the rank of the target group is sufficiently large. However, it is also known to fail in a number of small-rank examples. Describing all the situations in which the conjecture holds thus becomes an interesting problem.

The talk will begin with a brief overview of the main ingredients: the local theta correspondence and local Arthur packets. After formulating the conjecture, I will present new results which provide an answer to the above question. This is joint work with Marcela Hanzer.