Ugo Piomelli (Queen’s)

Date

Tuesday March 5, 2024
9:30 am - 10:30 am

Location

Jeffery Hall, Room 319 (Via Zoom)

PDEs & Applications Seminar

Tuesday, March 5th, 2024

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319 (Via Zoom)

Speaker: Ugo Piomelli (Queen’s)

Title: Numerical simultions of turbulence

Abstract: Turbulence has been described as the last unsolved problem of classical mechanics. It is a phenomenon that affects most fluid flows in engineering and the natural sciences, and its understanding is crucial to improve the design of ship, aircraft, and cars, the prediction of weather patterns, or the impact of environmental changes. Turbulence is a multiscale phenomenon, and is neither entirely deterministic, nor completely stochastic. While statistical mechanics tools can be used to predict the behaviour of the small and intermediate-sized motions, no theory has fully explained the behaviour of the larger ones, which depend strongly on the boundary conditions. Yet, it is the larger scales that drive the momentum and energy transport.

The numerical solution of the equations of motion, the Navier-Stokes equations, is a viable alternative to theory; however, the computational resources required for simulations of complex flows have been a limiting factor. The increased availability of computational resources and the development of new algorithms has made it possible, in recent years, to approach more realistic problem. High-fidelity simulations have resulted in better understanding of the physics, and, in turn, in the development of more accurate lower-level models for industrial design.

In this talk the challenges associated with the simulation of turbulent flows will be discussed. The most common numerical methods will be presented, with their advantages and disadvantages. A series of illustrative examples from Piomelli's research group will then be presented.

(Short) Bio: Ugo Piomelli obtained a Laurea in Ingegneria Aeronautica from the Università di Napoli "Federico II" in 1979. He then earned a Master of Science Degree in Aerospace Engineering from the University of Notre Dame in 1984 and a PhD in Mechanical Engineering from Stanford University in 1988. From 1987 to 2008 he was on the faculty of the Department of Mechanical Engineering at the University of Maryland, first as Assistant, then Associate and finally Full Professor. He served as Associate Chair and Director of Graduate studies from 2002 to 2007. In August 2008 he joined the Department of Mechanical and Materials Engineering at Queen’s University in Kingston, Ontario, where he held, from 2008 to 2022, the Tier 1 Canada Research Chair in Turbulence Simulation and Modelling.

Professor Piomelli has published over 100 refereed journal articles in the fields of turbulence and transition modelling and simulation. His work has been cited over 24,400 times, and he has an h-index of 55 (Google Scholar). He was elected Fellow of the Royal Society of Canada in 2015, of the Canadian Academy of Engineering in 2021, of the American Society of Mechanical Engineers in 2009, of the Institute of Physics (UK) in 2004 and of the American Physical Society in 2002. Since 2015, he has been the Editor-in-Chief of the Journal of Turbulence. His present research includes studies of the flow in rivers and lakes, turbulent boundary layers over smooth and rough surfaces, model development for large-eddy simulations, and flows in hydro-electric turbines and aeronautical applications.

Deepanshu Prasad

Date

Thursday February 29, 2024
4:00 pm - 5:00 pm

Location

Jeffery Hall, Room 319

Curves Seminar

Thursday, February 29th, 2024

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Deepanshu Prasad

Title: Seed Patterns of Type B_n and C_n are of Finite Type.

Abstract: We'll finish our discussion on folding and use the folding technique to prove that seed patterns, or the associated cluster algebra, of type B_n and C_n are of finite type.

Ivan Dimitrov (Queen's University)

Date

Thursday February 29, 2024
5:30 pm - 6:30 pm

Location

Jeffery Hall, Room 118

Math Club

Thursday, February 29th, 2024

Time: 5:30 p.m.  Place: Jeffery Hall, Room 118

Speaker: Ivan Dimitrov (Queen's University)

Title: Proof of the sensitivity conjecture

Abstract: IIn 2019 Hao Huang proved that, if $P$ is a set of $2^{n−1} + 1$ vertices of an $n$-dimensional cube, it contains a vertex with at least $\sqrt{n}$ neighbours in $P$.

This settled the nearly 30-year-old Sensitivity Conjecture.

We will discuss the conjecture, and see Huang’s proof.

Brian Hall (University of Notre Dame)

Date

Friday March 1, 2024
2:30 pm - 3:30 pm

Location

Jeffery Hall, Room 234

Math & Stats Department Colloquium

Friday, March 1st, 2023

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Brian Hall (University of Notre Dame)

Title: Heat flow on polynomials with connections to random matrix theory

Abstract: Here is a simple question with a surprisingly rich answer: How do the roots of a polynomial change as the polynomial evolves according to the heat equation? The simplest case of this question concerns the backward heat flow on polynomials with all real roots. In this case, an old theorem of P´olya and Benz says that the roots will remain real. Much more recent results tell us how these real roots evolve in the high-degree limit—and there is a surprising connection to random matrix theory. Things become even more interesting when we study the heat flow (forward or backward) on polynomials with complex roots. I will present some recent conjectures and rigorous results on this question. This is joint work with Ching Wei Ho, Jonas Jalowy, and Zakhar Kabluchko. The talk will be self-contained and have lots of pictures and animations.

Bio: Brian Hall received his Ph.D. from Cornell University in 1993 under Leonard Gross and is currently a professor at the University of Notre Dame. He is the author of two textbooks in the Graduate Texts in Mathematics series, Quantum Theory for Mathematicians and Lie Groups, Lie Algebras and Representations. His recent interests concern random matrices, random polynomials, and free probability.

 

Nicola de Nitti (EPFL)

Date

Tuesday February 13, 2024
9:30 am - 10:30 am

Location

Jeffery Hall, Room 319 (Via Zoom)

PDEs & Applications Seminar

Tuesday, February 13th, 2024

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319 (Via Zoom)

Speaker: Nicola de Nitti (EPFL)

Title: Sharp bounds on enstrophy growth for viscous scalar conservation laws

Abstract: We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admissible by the $L^\infty$ and total variation bounds and viscosity. This answers a conjecture by D. Ayala and B. Protas (Physica D, 2011), based on numerical evidence, for the viscous Burgers equation. This talk is based on a joint work with D. Albritton [https://doi.org/10.1088/1361-6544/ad073f].

Agnid Banerjee (ASU)

Date

Tuesday February 27, 2024
9:30 am - 10:30 am

Location

Jeffery Hall, Room 319 (Via Zoom)

PDEs & Applications Seminar

Tuesday, February 27th, 2024

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319 (Via Zoom)

Speaker: Agnid Banerjee (ASU)

Title: Space like strong unique continuation for some fractional parabolic equations

Abstract: My lecture will focus on a very classical subject: when do the zeros of a solution to a PDE spread? I will start with a brief historic overview. Then I will talk on some recent work of mine on space like strong unique continuation for fractional heat type equations which is joint with Vedansh Arya, Donatella Danielli and Nicola Garofalo.

M. Ram Murty (Queen's University)

Date

Monday February 26, 2024
2:30 pm - 3:30 pm

Location

Jeffery Hall, Room 202

Number Theory Seminar

Monday, February 26th, 2024

Time: 2:30 p.m.  Place: Jeffery Hall, Room 202

Speaker: M. Ram Murty (Queen's University)

Title: THE WIENER-IKEHARA TAUBERIAN THEOREM REVISITED

Abstract: The celebrated Wiener-Ikehara Tauberian theorem is a versatile result used in analytic number theory to produce "instant asymptotic formulas" simply from knowing analytic continuation of associated Dirichlet series. We will give a new proof of this result using Fourier analysis. Our method also produces an error term which the classical approach does not. This is joint work with Jagannath Sahoo and Akshaa Vatwani at IIT Gandhinagar.

Matilde Lalin (Universite de Montreal)

Date

Friday February 23, 2024
2:30 pm - 3:30 pm

Location

Jeffery Hall, Room 234

Math & Stats Department Colloquium

Friday, February 23rd, 2023

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Matilde Lalin (Universite de Montreal)

Title: Sums of the divisor function and random matrix distributions

Abstract: The divisor function gives the number of positive divisors of a natural number. How can we go about understanding the behavior of this function when going over the natural numbers? In this talk we will discuss strategies to better understand this function, issues related to the distribution of these values, and connections to the Riemann zeta function and some groups of random matrices. This talk includes joint work with Vivian Kuperberg.

Bio: Prof. Matilde Lal´ın received her PhD from the University of Texas in Austin. She then held post-doctoral positions at the IAS and UBC, and a tenure-track position at the University of Alberta before joining the Universit´e de Montr´eal in 2010. Prof. Lal´ın is currently a CRM distinguished research scholar, she is a fellow of the CMS, the AMS and the AWM. She received the Krieger-Nelson Prize in 2022 and a Liftoff Fellowship from the Clay Mathematics Institute in 2005.

 

Karl Dilcher (Dalhousie University)

Date

Friday February 23, 2024
4:00 pm - 5:00 pm

Location

Jeffery Hall, Room 422

Number Theory Seminar

Friday, February 23rd, 2024

Time: 4:00 p.m.  Place: Jeffery Hall, Room 422

Speaker: Karl Dilcher (Dalhousie University)

Title: Heronian triangles, Gauss primes, and some linear recurrences

Abstract: We will see that certain sequences of Heronian triangles, that is, triangles with sides of integer length and with integer area, occur in an unexpected way in the study of some specific factorials. In particular, we will consider the multiplicative order of ((p-1)/4)! modulo a prime p = 1 (mod 4). The question of when this order can be a power of 2 leads to the concept of a "Gauss prime". Apart from explaining these various connections, I will derive some divisibility properties of the sequences in question.

Time allowing, I will also discuss factorials ((p-1)/3)! modulo primes p = 1 (mod 6), and generalizations of such factorials. Quite recently, a close relationship between "exceptional primes" in this setting and Iwasawa theory was established by M. Stokes in his Ph.D. thesis. (Joint work with John Cosgrave.)

Luke Steverango

Date

Thursday February 15, 2024
4:00 pm - 5:00 pm

Location

Jeffery Hall, Room 319

Curves Seminar

Thursday, February 15th, 2024

Time: 4:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Luke Steverango

Title: Folding

Abstract: Folding is a process that allows us to create new seed patterns from existing ones. We will construct a quotient object, which arises from considering the symmetries of the associated quiver to a cluster algebra. This technique will be useful when we attempt to prove that cluster algebras of type B,C,F,G are of finite type.