L3

We model the trading strategy of an investor who spoofs the limit order book (LOB) to increase the revenue obtained from selling a position in a security. The strategy employs, in addition to sell limit orders (LOs) and sell market orders (MOs), a large number of spoof buy LOs to manipulate the volume imbalance of the LOB. Spoofing is illegal, so the strategy trades off the gains that originate from spoofing against the expected financial losses due to a fine imposed by the financial authorities. As the expected value of the fine increases, the investor relies less on spoofing, and if the expected fine is large enough, it is optimal for the investor not too spoof the LOB because the fine outweighs the benefits from spoofing. The arrival rate of buy MOs increases because other traders believe that the spoofed buy-heavy LOB shows the true supply of liquidity and interpret this imbalance as an upward pressure in prices. When the fine is low, our results show that spoofing considerably increases the revenues from liquidating a position. The profit of the spoof strategy is higher than that of a no-spoof strategy for two reasons. First, the investor employs fewer MOs to draw the inventory to zero and benefits from roundtrip trades, which stem from spoof buy LOs that are ‘inadvertently’ filled and subsequently unwound with sell LOs. Second, the midprice trends upward when the book is buy-heavy, therefore, as time evolves, the spoofer sells the asset at better prices (on average).

The Aldous diffusion is a conjectured Markov process on the
space of real trees that is the continuum analogue of discrete Markov
chains on binary trees. We construct this conjectured process via a
consistent system of stationary evolutions of binary trees with k
labelled leaves and edges decorated with diffusions on a space of
interval partitions constructed in previous work by the same authors.
This pathwise construction allows us to study and compute path
properties of the Aldous diffusion including evolutions of projected
masses and distances between branch points. A key part of proving the
consistency of the projective system is Rogers and Pitman’s notion of
intertwining. This is joint work with Noah Forman, Soumik Pal and
Douglas Rizzolo.                            

 I will talk about optimal estimates for stochastic integrals
in the case when both rough paths and martingales play a role.

This is an ongoing joint work with Peter Friz (TU Berlin).

We derive generalized lower Ricci bounds in terms of signed measures. And we prove associated gradient estimates for the heat flow with Neumann boundary conditions on domains of metric measure spaces obtained through „convexification“ of the domains by means of subtle time changes. This improves upon previous results both in the case of non-convex domains and in the case of convex domains.
 

"We consider a spatial Lambda-Fleming-Viot process, a model in mathematical biology, with a randomly chosen (rough) selection field. We study the scaling limit of this process in different regimes. This leads to the analysis of semi-discrete approximations of singular SPDEs, in particular the Parabolic Anderson Model and allows to extend previous results to weakly nonlinear cases. The subject presented is based on joint works with Aleksander Klimek and Nicolas Perkowski."

In this talk I will introduce a continuous wetting model consisting of the law of a Brownian meander tilted by its local time at a positive level h, with h small. I will prove that this measure converges, as h tends to 0, to the same weak limit as for discrete critical wetting models. I will also discuss the corresponding gradient dynamics, which is expected to converge to a Bessel SPDE admitting the law of a reflecting Brownian motion as invariant measure. This is based on joint work with Jean-Dominique Deuschel and Tal Orenshtein.

We discuss the models of random geometry that are derived
from scaling limits of large graphs embedded in the sphere and
chosen uniformly at random in a suitable class. The case of
quadrangulations with a boundary leads to the so-called
Brownian disk, which has been studied in a number of recent works.
We present a new construction of the Brownian
disk from excursion theory for Brownian motion indexed
by the Brownian tree. We also explain how the structure
of connected components of the Brownian disk above a
given height gives rise to a remarkable connection with
growth-fragmentation processes.

We exhibit a new martingale coupling between two probability measures $\mu$ and $\nu$ in convex order on the real line. This coupling is explicit in terms of the integrals of the positive and negative parts of the difference between the quantile functions of $\mu$ and $\nu$. The integral of $|y-x|$ with respect to this coupling is smaller than twice the Wasserstein distance with index one between $\mu$ and $\nu$. When the comonotonous coupling between $\mu$ and $\nu$ is given by a map $T$, it minimizes the integral of $|y-T(x)|$ among all martingales coupling.

(joint work with William Margheriti)

I will discuss the origin of the choice of global structure
--- or equivalently, the choice for which higher p-form symmetries are
present in the theory --- for various (Lagrangian and non-Lagrangian)
field theories in terms of their realization in IIB and M-theory. I
will explain how this choice on the field theory side can be traced
back to the fact that fluxes in string/M-theory do not commute in the
presence of torsion. I will illustrate how these ideas provide a
stringy explanation for the fact that six-dimensional (2,0) and (1,0)
theories generically have a partition vector (as opposed to a partition
function) and explain how this reproduces the classification of N=4
theories provided by Aharony, Seiberg and Tachikawa. Time permitting, I
will also explain how to use these ideas to obtain the algebra of
higher p-form symmetries for 5d SCFTs arising from M-theory at
arbitrary isolated toric singularities, and to classify global forms
for various 4d theories in the presence of duality defects.

Neurodegenerative diseases such as Alzheimer’s or Parkinson’s are devastating conditions with poorly understood mechanisms and no known cure. Yet a striking feature of these conditions is the characteristic pattern of invasion throughout the brain, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies. In this talk, I will show that by linking new mathematical theories to recent progress in imaging, we can unravel some of the universal features associated with dementia and, more generally, brain functions. In particular, I will outline interesting mathematical problems and ideas that naturally appear in the process.