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IMA Annual Program Year Workshop

Modern Applications of Homology and Cohomology

Modern Applications of Homology and Cohomology

October 28 - November 1, 2013

University of Texas, Austin | |

University of Chicago | |

Peking University |

(Co)homology theories, and more specifically algebraic structures on the cochain complex, have recently surfaced in unexpected areas of applied mathematics. The concrete interpretation of the cochain complex as a discretization of differential forms was a key insight of Thom and Whitney from the 1950s. This viewpoint has recently found new application in reinterpreting the families of forms that appear in computational fluid mechanics and electrodynamics. More generally, there has been striking advances relating the cochain complex to questions of stability in finite element and finite volume methods.

An area that has seen a lot of exciting recent development is applications of Hodge-De Rham theory. Several variants of this have been applied in new ways to obtain surprising results in a wide variety of disparate areas, including cognitive science, computer graphics and vision, game theory, machine learning, numerical PDE, voting theory, sensor networks, and statistical ranking.

This workshop will serve as a gathering place for all those interested in the applications of homology and cohomology theories to science and engineering. We intend to provide a forum for applied practitioners from diverse areas to share ideas and also to provide a venue for working algebraic topologists (pure mathematicians) to be exposed to applied problems. We hope that the wide array of backgrounds and intended applications will productively intermingle perspectives and methodology.

Monday | Tuesday | Wednesday | Thursday | Friday | |||
---|---|---|---|

Monday October 28, 2013 | |||

8:00am-8:45am | Registration | Keller Hall 3-176 | |

8:45am-9:00am | Welcome | Keller Hall 3-180 | |

9:00am-9:50am | The Debye Source Representation for Solutions of Maxwell's Equations | Charles Epstein (University of Pennsylvania) | Keller Hall 3-180 |

9:50am-10:15am | Break | Keller Hall 3-176 | |

10:15am-11:05am | Measuring Distance Between Reeb Graphs | Yusu Wang (The Ohio State University) | Keller Hall 3-180 |

11:05am-11:30am | Break | Keller Hall 3-180 | |

11:30am-12:20pm | A Confluence of Algebraic Topology and Numerical Analysis | Douglas Arnold (University of Minnesota, Twin Cities) | Keller Hall 3-180 |

12:20pm-2:00pm | Lunch | ||

2:00pm-2:50pm | Information Geometry: From Divergence Function to Metric, Equiaffine, Symplectic, and Kahler Structures on a Manifold | Jun Zhang (University of Michigan) | Keller Hall 3-180 |

2:50pm-3:15pm | Break | Keller Hall 3-176 | |

3:15pm-4:05pm | The Abstract Hodge--Dirac Operator and its Stable Discretization | Ari Stern (Washington University) | Keller Hall 3-180 |

4:05pm-5:00pm | Discussion | Keller Hall 3-180 | |

6:00pm-8:00pm | Social Hour at Republic Restaurant website | 221 Cedar Avenue South - Minneapolis (Historical Seven Corners) | |

Tuesday October 29, 2013 | |||

8:30am-9:00am | Coffee | Keller Hall 3-176 | |

9:00am-9:50am | Dynamics in Near-Potential Games | Pablo Parrilo (Massachusetts Institute of Technology) | Keller Hall 3-180 |

9:50am-10:15am | Break | Keller Hall 3-176 | |

10:15am-11:05am | Using Harmonic Measures to Reveal Source Locations Under Random Walks | Jie Gao (State University of New York, Stony Brook (SUNY)) | Keller Hall 3-180 |

11:05am-11:15am | Group Photo | Keller Hall 3-180 | |

11:15am-11:30am | Break | Keller Hall 3-176 | |

11:30am-12:20pm | Exotic Configuration Spaces | Yuliy Baryshnikov (University of Illinois at Urbana-Champaign) | Keller Hall 3-180 |

12:20pm-2:00pm | Lunch | ||

2:00pm-2:50pm | Random Walks and Diffusion on Simplicial Complexes: From Coverage Verification to a Simplicial Page Rank | Ali Jadbabaie (University of Pennsylvania) | Keller Hall 3-180 |

2:50pm-3:15pm | Break | Keller Hall 3-176 | |

3:15pm-4:05pm | Hodge Theory for Metric Spaces | Thomas Schick (Georg-August-Universität zu Göttingen) | Keller Hall 3-180 |

4:05pm-6:00pm | Poster SessionLind Hall 400 | ||

Wednesday October 30, 2013 | |||

8:30am-9:00am | Coffee | Keller Hall 3-176 | |

9:00am-9:50am | Graph Induced Complex: A Data Sparsifier for Homology Inference | Tamal Dey (The Ohio State University) | Keller Hall 3-180 |

9:50am-10:15am | Break | Keller Hall 3-176 | |

10:15am-11:05am | Statistical Regularities of Self-Intersection Counts for Geodesics on Negatively Curved Surfaces | Steven Lalley (University of Chicago) | Keller Hall 3-180 |

11:05am-11:30am | Break | Keller Hall 3-176 | |

11:30am-12:20pm | A Nonlocal Vector Calculus and Nonlocal Balance Laws | Richard Lehoucq (Sandia National Laboratories) | Keller Hall 3-180 |

12:20pm-2:00pm | Lunch | ||

2:00pm-2:50pm | Space-Time Finite-Element Exterior Calculus and Variational Discretizations of Gauge Field Theories | Melvin Leok (University of California, San Diego) | Keller Hall 3-180 |

2:50pm-3:15pm | Break | Keller Hall 3-176 | |

3:15pm-4:15pm | Discussion | Keller Hall 3-180 | |

8:00pm-9:00pm | Informal Social Event | ||

Thursday October 31, 2013 | |||

8:30am-9:00am | Coffee | Keller Hall 3-176 | |

9:00am-9:50am | Algebraic Topology as Applied to a Problem in Statistical Mechanics | John Klein (Wayne State University) | Keller Hall 3-180 |

9:50am-10:15am | Break | Keller Hall 3-176 | |

10:15am-11:05am | On Operator Representations for Discrete Differential Geometry | Mirela Ben-Chen (Technion-Israel Institute of Technology) | Keller Hall 3-180 |

11:05am-11:30am | Break | Keller Hall 3-176 | |

11:30am-12:20pm | Homology and Cohomology in Visualization: From Vector Fields to Memory Reference Traces | Bei Wang (University of Utah) | Keller Hall 3-180 |

12:20pm-2:00pm | Lunch | ||

2:00pm-2:50pm | Combinatorial Laplacians on Infinite Graphs | Jozef Dodziuk (City University of New York) | Keller Hall 3-180 |

2:50pm-3:15pm | Break | Keller Hall 3-176 | |

3:15pm-4:05pm | Spectral Clustering Revisited | Misha Belkin (The Ohio State University) | Keller Hall 3-180 |

4:05pm-5:00pm | Discussion | Keller Hall 3-180 | |

8:00pm-9:00pm | Informal Social Event | ||

Friday November 01, 2013 | |||

8:30am-9:00am | Coffee | Keller Hall 3-180 | |

9:00am-9:50am | Random Walks on Simplicial Complexes and Cheeger Inqualities | Sayan Mukherjee (Duke University) | Keller Hall 3-180 |

9:50am-10:15am | Break | Keller Hall 3-180 | |

10:15am-11:05am | Vector Diffusion Maps and Random Matrices with Random Blocks | Hau-tieng Wu (Stanford University) | Keller Hall 3-180 |

11:05am-11:30am | Break | Keller Hall 3-176 | |

11:30am-12:30pm | Discussion | Keller Hall 3-180 |

NAME | DEPARTMENT | AFFILIATION |
---|---|---|

Henry Adams | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Leyda Almodóvar | Department of Mathematics | The University of Iowa |

Douglas Arnold | School of Mathematics | University of Minnesota, Twin Cities |

F. Javier Arsuaga | Department of Mathematics | San Francisco State University |

Yuliy Baryshnikov | Department of Mathematics | University of Illinois at Urbana-Champaign |

Somnath Basu | Department of Mathematical Sciences | Binghamton University (SUNY) |

Misha Belkin | Department of Computer Science and Engineering | The Ohio State University |

Greg Bell | Department of Mathematics and Statistics | University of North Carolina, Greensboro |

Mirela Ben-Chen | Department of Computer Science | Technion-Israel Institute of Technology |

Jesse Berwald | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Prasit Bhattacharya | Department of Mathematics | Indiana University |

Andrew Blumberg | Department of Mathematics | University of Texas, Austin |

Omer Bobrowski | Department of Mathematics | Duke University |

Robert Bruner | Department of Mathematics | Wayne State University |

Peter Bubenik | Department of Mathematics | Cleveland State University |

Yiqing Cai | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Gunnar Carlsson | Department of Mathematics | Stanford University |

Chao Chen | Department of Computer Science | Rutgers, The State University Of New Jersey |

Eungchun Cho | Department of Mathematics | Kentucky State University |

Frederick Cohen | Department of Mathematics | University of Rochester |

Armindo Costa | Mathematics Institute | University of Warwick |

Isabel Darcy | Department of Mathematics | The University of Iowa |

Vin de Silva | Department of Mathematics and Computer Science | Pomona College |

Tamal Dey | Department of Computer Science and Engineering | The Ohio State University |

Yogeshwaran Dhandapani | Department of Electrical Engineering | Technion-Israel Institute of Technology |

Pawel Dlotko | Department of Mathematics | University of Pennsylvania |

Jozef Dodziuk | Department of Mathematics | City University of New York |

Charles Epstein | Department of Mathematics | University of Pennsylvania |

Lisbeth Fajstrup | Department of Mathematical Sciences | Aalborg University |

Michael Farber | Mathematics Institute | University of Warwick |

Brittany Fasy | Department of Computer Science | Tulane University |

Erica Flapan | Department of Mathematics | Pomona College |

Greg Friedman | Department of Mathematics | Texas Christian University |

Jie Gao | Department of Computer Science | State University of New York, Stony Brook (SUNY) |

Andrew Gillette | Department of Mathematics | University of Arizona |

Chad Giusti | Department of Mathematics | University of Nebraska |

Robert Hank | School of Mathematics | University of Minnesota, Twin Cities |

Minh Ha Quang | Pattern Analysis and Computer Vision | Istituto Italiano di Tecnologia |

Michael Hill | Department of Mathematics | University of Virginia |

Anil Hirani | Department of Mathematics | University of Illinois at Urbana-Champaign |

Annette Honken | Department of Mathematics | The University of Iowa |

Ali Jadbabaie | Department of Electrical and Systems Engineering | University of Pennsylvania |

Niles Johnson | Department of Mathematics | The Ohio State University |

Kaushik Kalyanaraman | Department of Computer Science | University of Illinois at Urbana-Champaign |

Jisu Kim | Department of Statistics | Carnegie Mellon University |

John Klein | Department of Mathematics | Wayne State University |

Joe Klobusicky | Department of Applied Mathematics | Brown University |

Irina Kogan | Department of Mathematics | North Carolina State University |

Hamid Krim | Department of Electrical and Computer Engineering | North Carolina State University |

Bala Krishnamoorthy | Department of Mathematics | Washington State University |

Steven Lalley | Department of Statistics | University of Chicago |

Tyler Lawson | School of Mathematics | University of Minnesota, Twin Cities |

Richard Lehoucq | Computational Mathematics and Algorithms | Sandia National Laboratories |

Melvin Leok | Department of Mathematics | University of California, San Diego |

Michael Lesnick | Institute for Mathematics and its Applications | Institute for Advanced Study |

Ji Li | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Lek-Heng Lim | Department of Statistics | University of Chicago |

Junwei Lu | Deptartment of Operations Research and Financial Engineering | Princeton University |

Anders Lundman | Department of Mathematics | Royal Institute of Technology (KTH) |

Greg Malen | Department of Mathematics | The Ohio State University |

Michael Mandell | Department of Mathematics | Indiana University |

Facundo Mémoli | Department of Mathematics | The Ohio State University |

Konstantin Mischaikow | Department of Mathematics | Rutgers, The State University Of New Jersey |

Anthea Monod | Department of Electrical Engineering | Technion-Israel Institute of Technology |

Sayan Mukherjee | Department of Statistical Science | Duke University |

Elizabeth Munch | Institute for Mathematics and its Applications | University of Minnesota Twin Cities |

Justin Noel | Bonn Topology Group | Max-Planck-Institut für Mathematik |

Sebastian Öberg | Department of Mathematics | Royal Institute of Technology (KTH) |

Carl Olimb | Department of Mathematics and Computer Science | Southwest Minnesota State University |

Christopher Palmer | School of Mathematics | University of Edinburgh |

Jun Yong Park | School of Mathematics | University of Minnesota, Twin Cities |

Pablo Parrilo | Department of Electrical Engineering and Computer Science | Massachusetts Institute of Technology |

Amit Patel | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Giovanni Petri | Department of Mathematical Sciences | ISI Foundation |

Peter Polacik | School of Mathematics | University of Minnesota, Twin Cities |

Martin Raussen | Department of Mathematical Sciences | Aalborg University |

Pedro Real-Jurado | Department of Applied Mathematics | University of Sevilla |

Antonio Rieser | Department of Mathematics | Technion-Israel Institute of Technology |

Thomas Schick | Mathematisches Institut | Georg-August-Universität zu Göttingen |

Mark Schubel | Department of Physics | University of Illinois at Urbana-Champaign |

Martina Scolamiero | Department of Mathematics | Royal Institute of Technology (KTH) |

Marko Seslija | Department of Electrical Engineering | Katholieke Universiteit Leuven |

Ankit Sharma | Computer Science | University of Minnesota, Twin Cities |

Nat Smale | Department of Mathematics | University of Utah |

John Steenbergen | Department of Mathematics | Duke University |

Ari Stern | Department of Mathematics | Washington University |

De Witt Sumners | Department of Mathematics | Florida State University |

Jian Sun | Mathematical Sciences Center | Tsinghua University |

Wan Tang | Department of Biostatistics and Computational Biology | University of Rochester |

Krystal Taylor | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Yiying Tong | Department of Computer Science and Engineering | Michigan State University |

Mariel Vazquez | Department of Mathematics | San Francisco State University |

Mikael Vejdemo-Johansson | Computer Vision and Active Perception Lab | Royal Institute of Technology (KTH) |

Andrea Villa | Department of Mathematical Sciences | ISI Foundation |

Alexander A. (Sasha) Voronov | School of Mathematics | University of Minnesota, Twin Cities |

Bei Wang | Scientific Computing and Imaging Institute | University of Utah |

Han Wang | Department of Mathematics | University of Illinois at Urbana-Champaign |

Ke Wang | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Yusu Wang | Department of Computer Science and Engineering | The Ohio State University |

Craig Westerland | School of Mathematics | University of Minnesota, Twin Cities |

Ragnar Winther | Centre of Mathematics for Applications | University of Oslo |

Matthew Wright | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Hau-tieng Wu | Department of Statistics | Stanford University |

Jiechao Xiong | Beijing International Center for Mathematical Research | Beijing (Peking) University |

Qianqian Xu | Beijing International Center for Mathematical Research | Peking University |

Bowei Yan | School of Mathematical Science | Peking University |

Yuan Yao | School of Mathematical Sciences | Peking University |

Ke Ye | Department of Mathematics | University of Chicago |

Jun Zhang | Department of Psychology and Department of Mathematics | University of Michigan |

Tianqi Zhao | Operations Research and Financial Engineering | Princeton University |

Zhizhen (Jane) Zhao | Courant Institute of Mathematical Sciences | New York University |

Xiaojin (Jerry) Zhu | Department of Computer Science | University of Wisconsin, Madison |

Lori Ziegelmeier | Department of Mathematics | Macalester College |

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