Dominic Veconi
Pennsylvania State University
I received my Ph.D. in mathematics from the Pennsylvania State University in 2021. My dissertation research was in the field of thermodynamic formalism and smooth ergodic theory for nonuniformly hyperbolic and singular hyperbolic dynamical systems. I am now a postdoctoral fellow at the Abdus Salam International Centre for Theoretical Physics, where I continue to do research on smooth ergodic theory and nonuniform hyperbolicity.
Dynamical Systems
Dynamical systems is the general area of mathematics that examines how points in a space change over time. Any system that consists of a set of points in space, and a rule by which these points move, is a dynamical system. The origins of the field can be traced back to Isaac Newton's Three-Body Problem, and its modern incarnation has grown out of the work of nineteenth- and twentieth-century mathematicians and physicists, such as Henri Poincaré, William Rowan Hamilton, Ludwig Boltzmann, and many others.
Within dynamical systems, ergodic theory uses tools and techniques from dynamics to examine statistical properties of random data as the data changes over time. Many classical dynamical systems, such as the Three-Body Problem and basic models of atmospheric convection, are of such high complexity that their long-term behavior mathematically cannot be predicted with 100% accuracy (consider how the weather today may tell us about the weather tomorrow, but tells us nothing about the weather in three weeks). However, despite the "chaotic" nature of such dynamical systems, the statistical behavior of different solutions is often highly predictable. Using this framework, ergodic theory examines the statistical behavior of otherwise "unpredictable" dynamical systems.
My Role in IMM
My role in the IMM is twofold. I write the exams and homework for the class in Complex Analysis, and I hold tutorial sessions and office hours with the students regularly throughout the week. Complex analysis is the study of complex numbers and complex-differentiable functions, and is an incredibly rich and beautiful area of mathematics. Some of the most elegant results in mathematics come from complex analysis, from Euler's formula for complex exponentiation to Cauchy's theorem and its consequences for integration. In addition to these purely mathematical results, complex numbers and holomorphic functions are fundamental to biology, electromagnetism, mechanics, and particle physics. It's a pleasure and a privilege to share this field with dedicated mathematics students from around the world.I am from Italy and I am currently a CNRS researcher working in Lille, France. After my undergraduate studies in Pisa, I did my PhD studies in Pisa and Toulouse. I was later postdoc in London before joining CNRS in France.