The spring 2023 Ritt Lectures will take place on Monday, April 17, 2023 and Friday, April 21, 2023 from 4:45 – 5:45pm. Professor Camillo De Lellis (Institute for Advanced Study), will deliver a two talk series titled: ‘Areaminimizing integral currents: singularities and structure’.
Abstract: Areaminimizing integral currents are a natural generalization of areaminimizing oriented surfaces. The concept was pioneered by De Giorgi for hypersurfaces of the Euclidean space, and extended by Federer and Fleming to any codimension and general Riemannian ambients. These classical works of the fifties and sixties establish a general existence theory for the oriented Plateau problem of finding surfaces of least area spanning a given contour.
Celebrated examples of singular 7dimensional minimizers in R^8 and of singular 2dimensional minimizers in R^4 are known since long and in fact in these cases there is no smooth oriented minimizer and any smooth minimizing sequence converges to the singular ones in an appropriate sense. A first theorem which summarizes the work of several mathematicians in the 60es and 70es (De Giorgi, Fleming, Almgren, Simons, and Federer) and a second theorem of Almgren from 1980 give dimension bounds for the singular set which match the one of the examples, in codimension 1 and in general codimension respectively.
In these lectures I will focus on the case of general codimension and address the question of which structural results can be further proved for the singular set. A recent theorem by Liu proves that the latter can in fact be a fractal of any Hausdorff dimension \alpha \leq m2. On the other hand it seems likely that it is an(m2)rectifiable set, i.e. that it can be covered by countably many C^1submanifolds leaving aside a set of zero (m2)dimensional Hausdorff measure. This conjecture is the counterpart, in general codimension, of a celebrated work of Leon Simon in the nineties for the codimension 1 case. In these lectures I will explain why the problem is very challenging, how it can be broken down into easier pieces, and present a line of attack based on recent joint works with Anna Skorobogatova and Paul Minter.
Dates: Monday, April 17, 2023 (4:30pm start time on Monday)
Friday, April 21, 2023 from 4:45 – 5:45pm
Location: Mathematics Hall, room 520
ColumbiaPrinceton Probability Day 2023
Friday, April 28, 2023
Location: Mathematics Hall, room 312
Annual oneday conference alternating between Columbia and Princeton.
Registration: Registration (which is free) can be done at this link. It is not required for attendance, but highly encouraged as it will help us arrange for food.
Speakers:
LouisPierre Arguin (CUNY)
Milind Hegde (Columbia)
Donghan Kim (Michigan)
Jinyoung Park (NYU)
Jacob Shapiro (Princeton)
Philippe Sosoe (Cornell)
Schedule:
9:00–10:10 Breakfast
10:00–10:50 LouisPierre Arguin
10:55–11:35 Jacob Shapiro
11:40–12:20 Donghan Kim
12:20–1:20 Lunch
1:20–2:10 Jinyoung Park
2:20–3:00 Milind Hegde
3:00–3:30 Tea
3:30–4:20 Philippe Sosoe
For further information, please contact the organizers, Milind Hegde or Ivan Corwin.
Free Boundary Problems: Lecture Series and Recent Advances in Theory and Applications
The goal of the workshop is to catalyze interactions among researchers working on various mathematical and physical aspects of free boundary problems. Featured in the research lectures will be PDE analysts, and applied and computational mathematicians working in the field, and also some researchers who will speak on physical experiments.
The workshop will consist of morning short course / pedagogical talks, aimed at graduate students and postdocs, and afternoon research talks.
This workshop is supported in part by NSF RTG Grant 1937254 and Simons Foundation Math + X Investigator Award #376319.
MiniCourse Speakers

Roberto Camassa (The University of North Carolina at Chapel Hill)

Enrico Valdinoci (The University of Western Australia)

Vlad Vicol (New York University)

Dallas Albritton (Princeton University)

Michele Coti Zelati (Imperial College London)

Donatella Danielli (Arizona State University)

Serena Dipierro (The University of Western Australia)

Javier GomezSerrano (Brown University)

Pavel Lushnikov (University of MinnesotaTwin Cities)

Antoine Mellet (University of Maryland)

Matthew Novack (Purdue University)

Stefania Patrizi (The University of Texas at Austin)

Pedro Saenz (The University of North Carolina at Chapel Hill)