Recently Added

Infinite staircases of symplectic embeddings of ellipsoids into Hirzebruch surfaces

Morgan Weiler
Rice University
June 5, 2020
Gromov nonsqueezing tells us that symplectic embeddings are governed by more complex obstructions than volume. In particular, in 2012, McDuff-Schlenk computed the embedding capacity function of the ball, whose value at a is the size of the smallest four-dimensional ball into which the ellipsoid E(1,a) symplectically embeds. They found that it contains an “infinite staircase” of piecewise-linear sections accumulating from below to the golden ratio to the fourth power. However, infinite staircases seem to be rare for more general targets.

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions

Florian Richter
Northwestern University
June 4, 2020
One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases.

Winding for Wave Maps

Max Engelstein
University of Minnesota
June 1, 2020
Wave maps are harmonic maps from a Lorentzian domain to a Riemannian target. Like solutions to many energy critical PDE, wave maps can develop singularities where the energy concentrates on arbitrary small scales but the norm stays bounded. Zooming in on these singularities yields a harmonic map (called a soliton or bubble) in the weak limit. One fundamental question is whether this weak limit is unique, that is to say, whether different bubbles may appear as the limit of different sequences of rescalings.

Mirrors of curves and their Fukaya categories

Denis Auroux
Harvard University
May 22, 2020
Homological mirror symmetry predicts that the derived category of coherent sheaves on a curve has a symplectic counterpart as the Fukaya category of a mirror space. However, with the exception of elliptic curves, this mirror is usually a symplectic Landau-Ginzburg model, i.e. a non-compact manifold equipped with the extra data of a "stop" in its boundary at infinity.

Joint equidistribution of adelic torus orbits and families of twisted L-functions

Farrell Brumley
Université Sorbonne Paris Nord
May 28, 2020
The classical Linnik problems are concerned with the equidistribution of adelic torus orbits on the homogeneous spaces attached to inner forms of GL2, as the discriminant of the torus gets large. When specialized, these problems admit beautiful classical interpretations, such as the equidistribution of integer points on spheres, of Heegner points or packets of closed geodesics on the modular surface, or of supersingular reductions of CM elliptic curves.

Will I Have to Mortgage My House? Reflections on Gene Therapy, Innovation, and Inequality

Eben Kirksey
Friends of the Institute Member, School of Social Science
May 15, 2020
The first FDA-approved gene therapy, Kymriah, was released to the public in August 2017 with a $475,000 price tag. With the emergence of personalized genetic medicine, we are entering a new era of profound inequality. This talk explores the stories of children and parents who signed up for the Kymriah clinical trial before it was approved--risking their lives and household finances in pursuit of a cancer cure. Issues of race and class played out at Penn Medicine, as researchers explored new horizons of hope with living cellular therapies.

Victorian Fiction and the Location of Experience

Adela Pinch
Visitor, School of Social Science
May 22, 2020
What do we mean by “experience”? How have philosophers sought to help us understand this essential category of human existence? And how have novelists and literary critics grappled with this category? This talk brings the tools of literary analysis to both Victorian novels and Victorian philosophy, in order to enrich our appreciation of “experience.” Authors featured included Charlotte Brontë and William James, but you will also be introduced to some lesser-known figures, such as Shadworth Hodgson and May Sinclair.

Forecasting Epidemics and Pandemics

Roni Rosenfeld
Carnegie Mellon University
May 21, 2020
Epidemiological forecasting is critically needed for decision making by national and local governments, public health officials, healthcare institutions and the general public. The Delphi group at Carnegie Mellon University was founded in 2012 to advance the theory and technological capability of epidemiological forecasting, and to promote its role in decision making, both public and private. Our long term vision is to make epidemiological forecasting as useful and universally accepted as weather forecasting is today.

Iwasawa theory and Bloch-Kato conjecture for unitary groups

Xin Wan
Morningside Center of Mathematics, Chinese Academy of Sciences
May 21, 2020
We describe a new method to study Eisenstein family and Iwasawa theory on unitary groups over totally real fields of general signatures. As a consequence we prove that if the central L-value of a cuspidal eigenform on the unitary group twisted by a CM character is 0, then the corresponding Selmer group has positive rank. The method also has a byproduct the p-adic functional equations for p-adic L-functions and p-adic families of Eisenstein series on unitary groups.