Spring School on Discrete and Computational Geometry

Simons Center for Geometry and Physics, April 17-21, 2017

The organizers are Chris Bishop and Joe Mitchell .

The workshop will feature four mini-courses:

Esther Ezra , Georgia Tech: Geometric Set Systems: Structures and Applications

David Mount, University of Maryland: Approximation Algorithms for Multidimensional Proximity Problems

Scott Sheffield , MIT: Random Geometric Structures: A Three-Lecture Overview

Yusu Wang , The Ohio State University: Mini-course on Computational Topology

There will also be a number of invited individual lectures by Chee Yap (Courant Institute), Joe Malkevitch (York College, CUNY), Hu Ding (Michigan State), Jie Gao (Stony Brook) and Boris Aronov (NYU), as well as student presentations, an open problem session and some social events.

Schedule:

PDF version with abstracts

Monday, April 17, 2017
12-12:45 SCGP lobby Registration
12:45-1 SCGP 103 Welcoming remarks, Alverez-Gaume, Lazarsfeld, Mitchell
1-2 SCGP 103 Mini-course Scott Sheffield - Random geometric structures: a three-lecture overview 1 VIDEO , SLIDES , (for all three talks)
2:30-3:30 SCGP 103 Mini-course Scott Sheffield - Random geometric structures: a three-lecture overview 2 VIDEO ,

Special lecture 4:00-5:00 Math P-131 V.M. Kharlamov of the University of Strasbourg, "Real Algebraic Enumerative Geometry: Invariant Counts and Their Qualitative Properties". This talk is not part of the SCGP workshop, but may be of interest to participants. ABSTRACT

Tuesday, April 18, 2017
9-10 SCGP 102 Mini-course Scott Sheffield - Random geometric structures: a three-lecture overview 3 VIDEO ,
10:30-11:30 SCGP 102 Mini-course Esther Ezra - Geometric Set Systems: Structures and Applications 1 VIDEO , LECTURE SLIDES , (for all three talks)
1-2 SCGP 103 SCGP Weekly Talk, Chee Yap - On Soft Foundations for Geometric Computation VIDEO , LECTURE SLIDES ,
2:30-3:30 SCGP 103 Mini-course Esther Ezra 2 - Geometric Set Systems: Structures and Applications 2 VIDEO ,
4-5 SCGP 102 Open Problem Session, BOARD SHOTS ,
7-9 Math S-240 Social event

Wednesday, April 19, 2017
9-10 SCGP 102 Mini-course Esther Ezra - Geometric Set Systems: Structures and Applications 3 VIDEO ,
11-12 SCGP 102 Mini-course Yusu Wang - Mini-course on computational topology 1 VIDEO , SLIDES ,
1-2 Math S-240 Math Club, Joe Malkevitch - Euler's Polyhedral Formula Still Inspires New Geometrical Results
2:30-3:30 SCGP 102 Mini-course Yusu Wang - Mini-course on computational topology 2 VIDEO ,
4-5 SCGP 102 Student Presentations:
4:00-4:20 Marc Khoury, Restricted Constrained Delaunay Triangulations
4:20-4:40 Sayan Bandyapadhyay, Effectiveness of Local Search for Art Gallery Problems, This talk is based on a recent joint work with Aniket Basu Roy
4:40-5:00 Sara Scaramuccia, A discrete Morse-based approach to multivariate data analysis

Thursday, April 20, 2017
9-10 SCGP 102 Mini-course Yusu Wang - Mini-course on computational topology 3 VIDEO ,
10:30-11:30 SCGP 102 Mini-course David Mount - Approximation Algorithms for Multidimensional Proximity Problems 1 VIDEO , SLIDES ,
1-2 SCGP 102 Invited lecture, Hu Ding - Simplex Lemma And The Applications in Data Analysis VIDEO ,
2:30-3:30 SCGP 102 Mini-course David Mount - Approximation Algorithms for Multidimensional Proximity Problems 2 VIDEO , SLIDES ,
4-5 SCGP 102 Math Department Colloquium, Jie Gao - Networking Applications of Curvature and Ricci Flow VIDEO ,

Friday, April 21, 2017
9-10 SCGP 102 Mini-course David Mount - Approximation Algorithms for Multidimensional Proximity Problems 3
10:30-11:30 SCGP 102 Invited lecture, Boris Aronov - Breaking depth-order cycles and other adventures in 3D VIDEO ,

Quantitative Finance lecture 11:30-12:30, SCGP 102, Maian Gidea (Yeshiva University) and Yuri Katz (S & P Global Market Intelligence) - "Topological data analysis of financial time series: landscapes of crashes". This talk is not part of the SCGP workshop, but may be of interest to participants. VIDEO ,
ABSTRACT: We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence homology to detect and quantify topological patterns that appear in multidimensional time series. Using a sliding window, we extract time-dependent point cloud data sets, to which we associate a topological space. We detect transient loops that appear in this space, and we measure their persistence. This is encoded in real-valued functions referred to as a "persistence landscapes". We quantify the temporal changes in persistence landscapes via their L p -norms. We test this procedure on multidimensional time series generated by various non-linear and non-equilibrium models. We find that, in the vicinity of financial meltdowns, the L p -norms exhibit strong growth prior to the primary peak, which ascends during a crash. Remarkably, the average spectral density at low frequencies of the time series of L p -norms of the persistence landscapes demonstrates a strong rising trend for 250 trading days prior to either dotcom crash on 03/10/2000, or to the Lehman bankruptcy on 09/15/2008. Our study suggests that TDA provides a new type of econometric analysis, which complements the standard statistical measures. The method can be used to detect early warning signals of imminent market crashes. We believe that this approach can be used beyond the analysis of financial time series presented here.

Additional materials related to the workshop

CSE 5559 : Computational topology: Theory, algorithms, and applications to data analysis This is a link to a course webpage taught by Professor Wang at Ohio State that is relevant to her mini-course at SCGP. The most relevant sections are topics 2--5, 8, and 11.

Local Information

Stony Brook Campus Map. The Simons Center is at the upper right corner of square 4B, the train station is in square 2B, and the hotel is in square 4D.

LIRR train schedule. The Stony Brook train station is on campus, about a five minute walk from the Simon Center.

Today's menu at the Simons Center Cafe. The full lunch includes 3 salad choices and a main course for $15-$20. There is usually a sandwich of the day for around $12. Iced tea and some flavored waters are included; bottled drinks are sold separately.

Other campus dining at list of locations and menus for student and retail dining on campus. The SAC is closest. East side dining a food court in a brand new dorm behind the Staller Center for the Arts and seems pretty good. Jasmine in the Wang center is cafeteria style Asian and Indian food.

The Hilton Garden Inn , website for the on-campus hotel. They also have a small restaurant.

The Bridgeport - Port Jefferson Ferry

Spring School on Discrete and Computational Geometry

Simons Center for Geometry and Physics, April 17-21, 2017

The workshop will feature four mini-courses:

Schedule:

Additional materials related to the workshop

Local Information

Off campus restaurants - walking distance

Off campus restaurants - Stony Brook Village - 10 minute drive - 30 minute walk

Off campus restaurants - Port Jefferson - 15 minute drive