The 2022 Gentry Lectures will be given by **Athanassios Spyridon Fokas,**** **Department of Applied Mathematics and Theoretical Physics (DAMTP) of the University of Cambridge. Dr. Fokas is a Greek mathematician with degrees in Aeronautical Engineering and Medicine. Since 2002, he has been a Professor of Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics at University of Cambridge.

**A Personal Journey through Complex Variables**

Tuesday, March 22 at 11 :00am

121 Manchester Hall and via Zoom

In the final year of my undergraduate studies in the department of Aeronautics at Imperial College, I became

aware that the so-called Wiener-Hopf technique was a particular case of a general problem in the theory of complex

variables known as a Riemann-Hilbert problem. Several years later, this connection allowed Mark Ablowitz and

myself to solve certain integrable nonlinear evolution PDEs. A generalization of this approach led to the development

of the powerful d-bar method. A deeper scrutiny of these developments by Israel Gelfand and myself led to a

unified approach for solving the initial values problem of linear and integrable nonlinear evolution PDEs as well as

to the solution of important problems arising in medical imaging. Unexpected new results in the theory of

complex variables also emerged.

**The two ‘big bangs’ of our mental evolution**

Tuesday, March 22 at 5:00pm

121 Manchester Hall and via Zoom

Visual perception is achieved via the deconstruction of a given percept followed by its reconstruction. I will refer

to the unconscious reconstruction of the percept as its mental representation. About a third of a second after an

unconscious reconstruction, the unconscious informs consciousness of the given percept. At this moment, the

first ‘big bang’ takes place: awareness. I will refer to the conscious construction of the percept as its mental image.

Many of our evolutionary predecessors possessed consciousness. So why do we differ from them qualitatively?

Many scholars have highlighted language as the key difference between us and other creatures possessing

consciousness. In my opinion, this is not entirely correct. Instead, I propose that we possess a predisposition to

construct real versions of our mental images and our mental representations, or to assign to them specific symbols.

I label the emerging constructions or symbols re-representations. This is the second ‘big bang’ of our mental

evolution which, in addition to language, includes the re-representations of mathematics, computers, technology,

and arts. Cubism will be used to illustrate the re-representation of arts.

**Bio:** Athanassios Spyridon Fokas is a Greek mathematician, with degrees in Aeronautical Engineering and Medicine. Since 2002, he has been a Professor of Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. (From Wikipedia.)

Fokas earned a BS in Aeronautics from Imperial College in 1975 and a PhD in Applied mathematics from Caltech in 1979. His dissertation, Invariants, Lie-Backlund Operators and Backlund Transformations, was written under the direction of Paco Axel Lagerstrom. He subsequently attended the Leonard M. Miller School of Medicine at the University of Miami, earning his medical degree in 1986.

After medical school, Fokas was appointed Professor and Chair of the Department of Mathematics and Computer Science at Clarkson University in 1986. From there, he moved to Imperial College in 1996 to a Chair of Applied Mathematics. Since 2002, he holds the Professorship of Nonlinear Mathematical Science (2000) in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, a professorship established in the year 2000 for a single tenure. He was elected a Member of the Academy of Athens in 2004 and a professorial fellow of Clare Hall, Cambridge in 2005.