Speaker: Bernard Nienhuis  (UL)
Title: Explicit conserved quantities of the XXZ quantum chain

Abstract: Conservation laws play a very fundamental role in physics. Thermodynamics
and hydrodynamics are founded on conservation principles. For many years I
have worked on integrable or solvable models. Thus I often heard the
statement that solvable models have extensively many conserved quantities.
But I never got to know them for any model. This made me curious to see
them explicitly.

Onno Huygens worked with me as a student on some version of the XXZ chain.
This is a solvable generalization of the one-dimensional Heisenberg model
for ferromagnetism, in which the interaction is anisotropic in spin space.
Out of curiosity I asked Onno to calculate the first 6 or so of its list
of conserved quantities. He succeeded, to get 8 of them. But as to be
expected, they get more complicated as you go down the list. So much so
that it is hard to learn anything from it.

Therefore I asked Onno to find common properties. For a few months he
found every week a few new properties all his 8 conserved quantities had
in common. Until at some day he walked into my office saying "I got them".
He meant that the properties he had found, were enough to define the
series, albeit as an algorithm, not as a closed form expression. Of course
we had no proof that the subsequent terms in the list still had the
propertied Onno had found. With massive computer power he was able to find
number 9 and 10, and they were correctly predicted by his algorithm.

Later, when Onno had moved on to other subjects, I discovered a possiblity
to write the list as a fairly simple closed form expression. This helped
to find a method to prove that they do indeed represent conserved
quantities. Still hard labor, but it worked.

In this talk I will of course introduce the XXZ chain. Then I will
illustrate the above history written by showing examples of the
ingredients of each of the steps in the progress. 

Location and time: JKH 2-3, Room 220 at 11-12.45

Afternoon session:

Speaker 1: Mirmukhsin Makhmudov (UL)

Title: Thermodynamic formalism for long-range potentials

Abstract: One-dimensional long-range models have captured considerable attention within the Statistical Mechanics

community, especially since F. Dyson demonstrated the presence of the phase transitions for long-range Ising models

in the low-temperature regime.

In 2017, A. Johansson, A. Öberg, and M. Pollicott studied the Dyson model on the half-line $\mathbb{\Z}$

and established that it also exhibits a phase transition, with a phase diagram similar to that of Dyson's classical model on $\mathbb{Z}$.

In this talk, I discuss the relationship between half-line and whole-line (classical) Gibbs states for one-dimensional

systems in a general setup.

Notably, the findings discussed apply to both ferromagnetic and

antiferromagnetic Dyson models. 

Additionally, the talk addresses the problem of the existence and regularity of the principal

eigenfunction of the Perron-Frobenius transfer operator for potentials that fall outside the studied classes in

Thermodynamic Formalism.

Location and time: JKH 2-3, Room 220, 14.15-15.00

Speaker 1: Hidde van Wiechem (TU Delft)

Title: A large deviation principle for run-and-tumble particles

Abstract: The run-and-tumble particle process is a toy model for active particles, which are particles that use internal energy to move in a preferred direction. We model this as a multi-layer process, where each layer represents an internal state,  to ensure that we are working with a Markov process. In this talk, we will investigate the scaling limits of the empirical measure of this model, with special focus on the large deviations. A main tool here is to introduce a weakly asymmetric version of the model, which produces the correct deviating paths for the large deviation principle. This talk is based on a joint work with Frank Redig and Elena Pulvirenti.

Location and time: JKH 2-3, Room 220, 15.15-16.00

This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.

 We are pleased to invite you to the Research Half Day on Mathematical Finance, 

taking place on March 18th, 2025, in the morning at Drift 25, Utrecht (Inner City). 

This event brings together researchers and professionals to discuss cutting-edge topics in financial mathematics.

Date: Tuesday, March 18th
Location: Drift 25, Utrecht
Time: 8:30 AM – 1:10 PM

Live stream: 

Meeting link: https://bit.ly/3WWuZAm

Meeting ID: 342 130 946 741

Toegangscode (Passcode): NR9yK7FZ

Program Schedule:

8:30 – 9:00 | Coffee & Welcome

9:00 – 9:50 | Laura Spierdijk (University of Twente)
Hedging the Unhedgeable? Pricing CAT Bonds in a Changing Climate

9:55 – 10:45 | Yilong Xu (Utrecht University)
A “Green Premium” or a “Brown Discount”: Evidence from Experimental Asset Markets

10:45 – 11:15 | Coffee Break

11:15 – 12:05 | Jaehyuk Choi (Columbia University)
Efficient Simulation of the SABR Model

12:10 – 13:00 | Michael Sanders (Rabobank, Utrecht)
Execution of Financial Products: How Quantitative Analysis Drives Decision-Making in Private Debt and Derivatives13:10 | Workshop Closing

Attendance is open to all, but registration is required. 

Please check the full program and register here: UU Events – Mathematical Finance Research Half Day.

We look forward to seeing you there!

This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.

This seminarwill explore important themes in modern homotopy theory, focusing onTopological Hochschild Homology (THH), Topological Cyclic Homology (TC), andtheir applications in algebraic K-theory, with a special emphasis on tracemethods.

Title:
Extremes in dynamical systems: max-stable and max-semistable laws

Abstract:
Extreme value theory for chaotic, deterministic dynamical systems is a rapidly expanding area of research. Given a dynamical system and a real-valued observable defined on its state space, extreme value theory studies the limit probabilistic laws for asymptotically large values attained by the observable along orbits of the system. Under suitable mixing conditions the extreme value laws are the same as those for stochastic processes of i.i.d. random variables.

Max-stable laws typically arise for probability distributions with regularly varying tails. However, in the context of dynamical systems, where the underlying invariant measure can be irregular, max-semistable distributions also have a natural place in studying extremal behaviour. In this talk I will first discuss a family of autoregressive processes with marginal distributions resembling the Cantor function. The resulting extreme value law can be proven to be a max-semistable distribution. Alternatively, we can describe the autoregressive process in terms of an iterated map with an invariant measure. Further examples of extreme value laws in dynamical systems are discussed as well.