6th Symposium on Analysis and PDEs

Purdue Bell Tower

Purdue University, June 1–4, 2015

Sixth in the series of the Symposia, going back to 2003

Principal Lecturers Invited Speakers Organizers Contributed Talks Financial Support Sponsors

Principal Lecturers

David Jerison (MIT)

Free Boundaries and Minimal Surfaces (minicourse)

Free boundaries arise as the interface between materials in which the materials retain some energy. In contrast, the interface represented by a minimal surface lives in an ambient space that is empty. Despite this difference between these two types of interfaces, there are deep connections between them. In a ground-breaking paper in 1980, Alt and Caffarelli showed that strategies and tools from the theory of minimal surfaces yield fundamental regularity theorems for free boundaries. The field has exploded since then.

In these lectures, we will start by explaining the wide family of energy functionals that can be treated by free boundary methods developed in that last 35 years. We will then focus on recent progress describing minimizers in higher dimensions and higher critical points in dimension 2. These are contexts in which free boundary problems return the favor by pointing to new insights into minimal surfaces.

Fang-Hua Lin (Courant Institute)

Extremum Problems for Elliptic Eigenvalues (minicourse)

In these lectures, we are going to discuss some simple but fundamental, extremum problems for Laplacian eigenvalues. They are interesting from both theory and applications. The goal of the lectures is to explain some relevant classical works and some recent thoughts on these problems.

Invited Speakers

Mark Allen (University of Texas at Austin)

Daniela De Silva (Columbia University)

Ailana Fraser (University of British Columbia)

Nikola Kamburov (University of Arizona)

Yuan Lou (Ohio State University)

Luis Silvestre (University of Chicago)

Hung Tran (University of Chicago)

Organizers

Donatella Danielli (Purdue University)

Arshak Petrosyan (Purdue University)

Aaron Yip (Purdue University)

Secretary: Julie Morris

Email: {This email is obscured. Your must have javascript enabled to see it}

Contributed Talks and Financial Support

Contributed talks (20 min) are being solicited. Preference will be given to graduate students and recent PhDs. To apply, please fill out Contributed Talk Request section on Registration page.

Financial support is available to graduate students, postdoctoral fellows and active senior researchers who do not have grants. People from the underrepresented groups (women and minorities) are particularly encouraged to apply. To apply, please fill out Financial Support Request section on Registration page.

IMA Participating Institution (PI) members may use IMA/PI funds to support travel of their personnel.

Thanks for your interest. Applications are now closed.

Sponsors

We gratefully acknowledge the support from National Science Foundation (NSF), Institute for Mathematics and its Applications (IMA) through its Participating Institution (PI) Program, and the Department of Mathematics, Purdue University.

NSF IMA Purdue University



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schedule

 Schedule  

Abstracts Schedule

All talks will be held in Lawson Computer Science Building (LWSN) 1142. Registration and coffee breaks will be in LWSN Commons area.

Monday, June 1

8:30—8:50 Registration and refreshments
8:50—9:00 Opening Remarks
9:00—9:50 Daniela De Silva, Barnard College, Columbia University
Higher Order Boundary Harnack Inequalities and Applications to Free Boundary Problems
10:00–10:50 Luis Silvestre, University of Chicago
C1,α regularity for the parabolic homogeneous p-Laplacian equation
11:00–11:30 Coffee Break
11:30–12:20 Mark Allen, University of Texas at Austin
Parabolic Problems with a Fractional Time Derivative
12:30–2:30 Lunch Break
2:30–3:20 Fang-Hua Lin, Courant Institute
Extremum Problems for Elliptic Eigenvalues – Lecture I
3:30–3:55 Rohit Jain, University of Texas at Austin
Randomly Homogenized Boundary Obstacle Problem
4:00–4:30 Coffee Break
4:30–4:55 Alessia Kogoj, University of Bologna
Weighted Lp-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups
5:00–5:25 Matias Delgadino, University of Maryland-College Park
The Relationship Between the Obstacle Problem and Minimizers of the Interaction Energy

Tuesday, June 2

8:30—9:00 Refreshments
9:00—9:50 David Jerison, Massachusetts Institute of Technology
Free Boundaries and Minimal Surfaces – Lecture I
10:00–10:50 Ailana Fraser, University of British Columbia
Minimal Surfaces and an Extremal Eigenvalue Problem
11:00–11:30 Coffee Break
11:30–12:20 Yuan Lou, Ohio State University
Asymptotic Behavior of the Smallest Eigenvalue of an Elliptic Operator and its Applications to Evolution of Dispersal
12:30–2:30 Lunch Break
2:30–3:20 Fang-Hua Lin, Courant Institute
Extremum Problems for Elliptic Eigenvalues – Lecture II
3:30–3:55 Robin Neumayer, University of Texas at Austin
A Strong Form of the Quantitative Wulff Inequality
4:00–4:30 Coffee Break
4:30–4:55 Eric Baer, Massachusetts Institute of Technology
Optimal Function Spaces for Continuity of the Hessian Determinant as a Distribution
5:00–5:25 Ryan Murray, Carnegie Mellon University
Second-Order Gamma Limit for the Cahn-Hilliard Functional
BANQUET Purdue Memorial Union (PMU) — North Ballroom
6:30 Cash Bar
7:00 Conference Dinner

Wednesday, June 3

8:30—9:00 Refreshments
9:00—9:50 David Jerison, Massachusetts Institute of Technology
Free Boundaries and Minimal Surfaces – Lecture II
10:00–10:50 Nikola Kamburov, University of Arizona
The Space of One-Phase Free Boundary Solutions in the Plane
11:00–11:30 Coffee Break
11:30–11:55 Max Engelstein, University of Chicago
A Free Boundary Problem for the Parabolic Poisson Kernel
12:00–12:25 Lyudmila Korobenko, McMaster University
Boundedness and Continuity of Solutions to Infinitely Degenerate Elliptic Equations via Sobolev Inequalities for Associated Metrics
12:30–2:30 Lunch Break
2:30–3:20 Fang-Hua Lin, Courant Institute
Extremum Problems for Elliptic Eigenvalues – Lecture III
3:30–3:55 Drew Swartz, Purdue University
Dynamics of a Second Order Gradient Model for Phase Transitions
4:00–4:25 Soledad Benguria, University of Wisconsin-Madison
The Brezis-Nirenberg Problem on Sn, in Spaces of Fractional Dimension
4:30–5:00 Refreshments

Thursday, June 4

8:30—9:00 Refreshments
9:00—9:50 David Jerison, Massachusetts Institute of Technology
Free Boundaries and Minimal Surfaces – Lecture III
10:00–10:25 Dennis Kriventsov, University of Texas at Austin
A Free Boundary Problem Related to Thermal Insulation
10:30–10:55 Veronica Quitalo, Purdue University
On a Long Range Segregation Model
11:00–11:30 Coffee Break
11:30–12:20 Hung Tran, University of Chicago
Some Inverse Problems in Periodic Homogenization of Hamilton-Jacobi Equations
12:30 Conference Ends


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registration

Symposium Registration

General Registration








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lodging

  Lodging  

The following blocks of rooms are reserved for the symposium participants (arrive 5/31, depart 6/4)

  • Union Club Hotel (10 min walking distance) – 25 rooms
    • Deadline to make a reservation: May 15th
    • Rate is $99/night + tax for standard queen room. Depending on the type of room and the number of guests, the rate could increase to $119/night + tax.
    • Block name: 6th Symposium on Analysis and PDEs
  • Hilton Garden Inn (23 min walking distance) – 15 rooms
    • Deadline to make a reservation: May 10th
    • Rate is $100/night + tax for either a king room (we have 8 in the block) or a room with 2 queen beds (we have 7 in the block).
    • Group Code: PDE
  • La Quinta Inn & Suites (23 min driving distance)
    • Rooms with either two queen or one king pillowtop beds.
    • Rate is $75/night + tax (breakfast included)
    • For reservations, please call 765-446-2400 and mention The 6th Annual PDE Symposium Rate
  • First Street Towers University Residence (11 min walking distance) – 40 rooms
    • Deadline to make a reservation: May 15th
    • Rate is $65/night + tax for a single room (double rooms are not available at this time).
    • For reservations, please contact Julie Morris at {This email is obscured. Your must have javascript enabled to see it}


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travel

Transportation to Purdue

(from Purdue University – Visitor Information)

Purdue is accessible from all modes of transportation, including

Plane Automobile Train Bus

By Plane + Shuttle Service

Purdue is accessible from the Indianapolis and Chicago O’hare international airports.

Indianapolis International Airport

Indianapolis International Airport (code: IND) is serviced by most major airlines and their partner airlines. Ground transportation to Purdue from the Indianapolis International Airport includes:

Shuttle Services

Rental Cars

Chicago O’hare International Airport

Chicago O’hare International Airport (code: ORD) is located approximately 140 miles north of Greater Lafayette and is approximately a 3 hour drive from the airport to Purdue. Ground transportation direct from the airport to campus is available from the shuttle services listed below.

Shuttle Services

By Automobile

From the South

Driving from the South (Indianapolis) West Lafayette is approximately 70 miles northwest of Indianapolis. Take I-65 North to Lafayette and exit on State Road 26 (exit 172). Turn left at the stop light on to State Road 26. Remain on State Rd 26 approx 5 miles. State Rd 26 follows South Street in Lafayette until you approach the downtown area. It then follows Columbia Street across the Wabash River. Once you cross the Wabash River, State Road 26 becomes State Street in West Lafayette. Proceed up State Street hill to Grant Street. Turn right on Grant Street, the Purdue Memorial Union will be on your left and the Grant Street Parking Garage will be on your right.

From the North

Driving from the North (Chicago) West Lafayette is approximately 140 miles southeast of Chicago. Take I-65 South to State Road 43 (exit 178). Turn right onto State Road 43. Drive South on State Road 43 (approximately 6 miles) to State St (State Road 26.) This will be the 4th stop light, and a McDonald’s will be on your right. Turn right onto State Street. You will want to remain in the right lane. Proceed up State Street hill to Grant Street ( 2nd stop light on State.) Turn right on Grant Street, the Purdue Memorial Union will be on your left and the Grant Street Parking Garage will be on your right.

By Train

Amtrak Train service to Lafayette is available from Indianapolis, Chicago, and several other cities. The most likely connection is via Chicago, and is described below. For directions from other departure points, consult Amtrak’s site. To get to the Amtrak Station or Greyhound Bus Terminal in Chicago from O’Hare Airport, take the Continental Express Shuttle (773 454-7800) to Union Station, 225 Canal Street, Chicago. For assistance, Continental’s uniformed ticket agents are located in the baggage claims areas of terminals 1, 2, and 3 as well as outside U.S. Customs in Terminal 5. From Union Station, take the Amtrak train bound for Lafayette, IN. It is best to book a seat in advance. The toll-free number is (800) 872-7245.

By Bus

Greyhound Bus services the Greater Lafayette area from the Chicago, Gary, Hammond, and Indianapolis hubs. Schedules and fares vary, so consult the Greyhound site or call 800-231-2222.



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