There are many constructions that yield C*-algebras. For example, we build them from groups, quantum groups, dynamical systems, and graphs. In this talk we look at C*-algebras that arise from a certain type of game. It turns out that the properties of the underlying game gives us very strong information about existence of traces of various types on the game algebra. The recent solution of the Connes Embedding Problem arises from a game whose algebra has a trace but no hyperlinear trace.

Assumed knowledge: Familiarity with tensor products of Hilbert spaces, the algebra of a discrete group, and free products of groups.

In this talk, we will review the notion of non-invertible symmetries and we will study adjoint QCD in two dimensions. It turns out that this theory has a plethora of such symmetries which require deconfinement in the massless case. When a mass or certain quartic interactions are tunrned on, these symmetries are broken and the theory confines. In addition, we will use these symmetries to calculate the string tension for small mass and make some comments about naturalness along the RG flow.

In 2010, Hrushovski--Loeser studied the homotopy type of the Berkovich analytification of a quasi-projective variety over a valued field. In this talk, we explore the extent to which some of their results might hold in a relative setting. More precisely, given a morphism of quasi-projective varieties over a valued field, we ask if we might construct deformation retractions of the analytifications of the source and target which are compatible with the analytification of the morphism and whose images are finite simplicial complexes. 

There has been a surge of interest in machine learning in the past few years, and deep learning techniques are more and more integrated into
the way we do quantitative science. A particularly exciting case for deep learning is molecular physics, where some of the "superpowers" of
machine learning can make a real difference in addressing hard and fundamental computational problems - on the other hand the rigorous
physical footing of these problems guides us in how to pose the learning problem and making the design decisions for the learning architecture.
In this lecture I will review some of our recent contributions in marrying deep learning with statistical mechanics, rare-event sampling
and quantum mechanics.

We propose a mathematical model that unifies the psychiatric concepts of drug-induced incentive salience (IST), reward prediction error

(RPE) and opponent process theory (OPT) to describe the emergence of addiction within substance abuse. The biphasic reward response (initially

positive, then negative) of the OPT is activated by a drug-induced dopamine release, and evolves according to neuro-adaptative brain

processes.  Successive drug intakes enhance the negative component of the reward response, which the user compensates for by increasing the

drug dose.  Further neuroadaptive processes ensue, creating a positive feedback between physiological changes and user-controlled drug

intake. Our drug response model can give rise to qualitatively different pathways for an initially naive user to become fully addicted.  The

path to addiction is represented by trajectories in parameter space that depend on the RPE, drug intake, and neuroadaptive changes.

We will discuss how our model can be used to guide detoxification protocols using auxiliary substances such as methadone, to mitigate withdrawal symptoms.

If this is useful here are my co-authors:
Davide Maestrini, Tom Chou, Maria R. D'Orsogna

The talk will discuss the use of mathematical models for understanding targeted cancer therapies. One area of focus is the treatment of chronic lymphocytic leukemia with tyrosine kinase inhibitors. I will explore how mathematical approaches have helped elucidate the mechanism of action of the targeted drug ibrutinib, and will discuss how evolutionary models, based on patient-specific parameters, can make individualized predictions about treatment outcomes. Another focus of the talk is the use of oncolytic viruses to kill cancer cells and drive cancers into remission. These are viruses that specifically infect cancer cells and spread throughout tumors. I will discuss mathematical models applied to experimental data that analyze virus spread in a spatially structured setting, concentrating on the interactions of the virus with innate immune mechanisms that determine the outcome of virus spread.  

Human life expectancy has been increasing steadily over the last century but this has resulted in an increasing incidence of age-related chronic diseases. Over 60% of people over the age of 65 will suffer from more than one disease at the same time (multimorbidity) and 25-50% of those over 80 years old develop frailty, defined as an accumulation of deficits and loss of reserve. Multimorbidity and frailty have complex medical needs and are strongly associated with disability and hospitalization. However, current treatments are suboptimal with problems of polypharmacy due to the fact that each disease is treated individually. Geroprotectors target fundamental mechanisms of ageing common to multiple age-related diseases and shows promise in delaying the onset of multimorbidity and frailty in animal models. However, their clinical testing in patients has been challenging due to the high level of complexity in the mode of action of geroprotectors and in the way multimorbidity and frailty develop.

 The talk will give an overview of these problems and make the case for the use of AI approaches to solve some of those complex issues with a view of designing appropriate clinical trials with geroprotectors to prevent age-related multimorbidity and frailty and extend healthspan.

Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). These therapies generally achieve impressive short-term responses, that unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape and ignore the fact that treatments drive the evolution of resistance. Here we present an integrated theoretical, experimental and clinical approach to develop treatment strategies that specifically embrace cancer evolution. We will consider the importance of using treatment response as a critical driver of subsequent treatment decisions, rather than fixed strategies that ignore it. Through the integrated application of drug treatments and drug holidays we will illustrate that, evolutionary therapy can drive either tumor control or extinction. Our results strongly indicate that the future of precision medicine shouldn’t be in the development of new drugs but rather in the smarter evolutionary application of preexisting ones.

Bacteria use intercellular signalling, or quorum sensing (QS), to share information and respond collectively to aspects of their surroundings. The autoinducers that carry this information are exposed to the external environment. Consequently, they are affected by factors such as removal through fluid flow, a ubiquitous feature of bacterial habitats ranging from the gut and lungs to lakes and oceans.

We develop and apply a general theory that identifies and quantifies the conditions required for QS activation in fluid flow by systematically linking cell- and population-level genetic and physical processes. We predict that cell-level positive feedback promotes a robust collective response, and can act as a low-pass filter at the population level in oscillatory flow, responding only to changes over slow enough timescales. Moreover, we use our model to hypothesize how bacterial populations can discern between increases in cell density and decreases in flow rate.