# Mathematical Sciences Research Institute

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# Workshop

CANCELLED Introductory Workshop on Geometric Flows and Function Theory in Real and Complex Geometry September 11, 2006 - September 15, 2006
 Registration Deadline: September 04, 2006 over 7 years ago June 11, 2006 over 7 years ago
Parent Program: Geometric Evolution Equations and Related Topics
Organizers Bennett Chow, Peter Li and Gang Tian
Speaker(s)

## Show List of Speakers

Description

Various geometric evolution equations and function theory have the common goal of understanding the relations between the geometry, analysis, and topology of manifolds, submanifolds, vector bundles, maps, and other geometric structures. The fields of geometry, analysis, and topology are synthesized through the study of geometric and topological invariants via a priori estimates. The goal of the Introductory Workshop is to survey current and recentdevelopments in geometric evolution equations and function theory in real and complex geometry. Invited speakers include: Albert Chau (University of Waterloo), Jaigyoung Choe (Seoul National University), Andre Neves (Princeton University), Lei Ni (University of California, San Diego), Natasa Sesum (New York University, Courant Institute), Jian Song (Johns Hopkins University), Jiaping Wang (University of Minnesota), Ben Weinkove (Imperial College, London), and Zhou Zhang (Massachusetts Institute of Technology). The talks will focus on the following topics:

1. Geometric flows in complex geometry
2. Function theory on manifolds
3. Ricci flow and canonical metrics
4. Mean curvature flow and applications

### Schedule of the Lectures

Monday September 11 9:30-10:30am Ben Weinkove: Geometric flows and moment maps, part I Tea Break 11am-12pm Jiaping Wang: Stability of harmonic functions  Abstract: We aim to explain a result of P. Li and L. Tam relating the harmonic functions to the number of ends of a complete manifold. We start with their constructive proof of the existence of Green's function, and use the result to show the stability of the space of harmonic functions under the perturbation within a compact domain. We then reach the conclusion by carrying out a straightforward construction of the so-called barrier function on each end. Lunch 2-3pm Andre Neves: Lagrangian mean curvature flow, part I Tea Break 3:30-4:30pm Natasa Sesum: Convergence and stability results for the Ricci flow, part I Tuesday September 12 9:30-10:30am Ben Weinkove: Geometric flows and moment maps, part II Tea Break 11am-12pm Jiaping Wang: Sharp estimate of Green's function and applications  Abstract: We will establish a sharp integral decay estimate of the minimal positive Green's function on a complete manifold with positive spectrum. Some applications will also be discussed. Lunch 2-3pm Natasa Sesum: Convergence and stability results for the Ricci flow, part II Tea Break 3:30-4:30pm Lei Ni: Ricci flow and invariant cones Wednesday September 13 9:30-10:30am Jaigyoung Choe: Rigidity of Capillary Surfaces and First Eigenvalue of Minimal Surfaces Tea Break 11am-12pm Andre Neves: Lagrangian mean curvature flow, part II Lunch No talks in the afternoon Thursday September 14 9:30-10:30am TBA Tea Break 11am-12pm Jian Song: The Kaehler-Ricci flow on surfaces, part I  Abstract: We study the Kaehler-Ricci flow on minimal surfaces of Kodaira dimension one and show that the flow collapses and converges to a unique canonical metric on its canonical model. Such a canonical metric is a generalized Kaehler-Einstein metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric classification for Kaeher surfaces with a numerically effective canonical line bundle by the Kaehler-Ricci flow. In general, we propose to find canonical metrics on the canonical models of projective varieties of positive Kodaira dimension. This is a joint work with G. Tian. Lunch 2-3pm Albert Chau: Uniformization of complete non-compact Kaehler manifolds and the Kaehler Ricci flow, part I Friday September 15 9:30-10:30am Jian Song: The Kaehler-Ricci flow on surfaces, part II Tea Break 11am-12pm Albert Chau: Uniformization of complete non-compact Kaehler manifolds and the Kaehler Ricci flow, part II Lunch 2-3pm Zhou Zhang: Kaehler-Ricci Flows over Manifolds of General Type

Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

MSRI has preferred rates at the Rose Garden Inn, depending on room availability. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show the MSRI rate on all room types available.

MSRI has preferred rates at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is $129 per night for a Deluxe Queen/King, based on availability. MSRI has preferred rates of$149 - $189 plus tax at the Hotel Shattuck Plaza, depending on room availability. Guests can either call the hotel's main line at 510-845-7300 and ask for the MSRI- Mathematical Science Research Inst. discount; or go to www.hotelshattuckplaza.com and click Book Now. Once on the reservation page, click “Promo/Corporate Code“ and input the code: msri. MSRI has preferred rates of$110 - \$140 at the Berkeley Lab Guest House, depending on room availability. Reservations may be made by calling 510-495-8000 or directly on their website. Select “I am an individual traveler affiliated with MSRI”.

Additional lodging options may be found on our short term housing page.

## Show Visa/Immigration

Schedule
Sep 11, 2006
Monday
 09:30 AM - 10:30 AM Geometric flows and moment maps, part I Ben Weinkove 11:00 AM - 12:00 PM Stability of harmonic functions Jiaping Wang 02:00 PM - 03:00 PM Lagrangian mean curvature flow, part I Andre Neves (Imperial College, London) 03:30 PM - 04:30 PM Convergence and stability results for the Ricci flow, part I Natasa Sesum (Rutgers University)
Sep 12, 2006
Tuesday
 09:30 AM - 10:30 AM Geometric flows and moment maps, part II Ben Weinkove 11:00 AM - 12:00 PM Sharp estimate of Green's function and applications Jiaping Wang 02:00 PM - 03:00 PM Convergence and stability results for the Ricci flow, part II Natasa Sesum (Rutgers University) 03:30 PM - 04:30 PM Ricci flow and invariant cones Lei Ni (University of California)
Sep 13, 2006
Wednesday
 09:30 AM - 10:30 AM TBA, part I Tom Ilmanen 11:00 AM - 12:00 PM Lagrangian mean curvature flow, part II Andre Neves (Imperial College, London)
Sep 14, 2006
Thursday
 09:30 AM - 10:30 AM TBA, part II Tom Ilmanen 11:00 AM - 12:00 PM The Kaehler-Ricci flow on surfaces, part I Jian Song 02:00 PM - 03:00 PM Uniformization of complete non-compact Kaehler manifolds and the Kaehler Ricci flow, part I Albert Chau
Sep 15, 2006
Friday
 09:30 AM - 10:30 AM The Kaehler-Ricci flow on surfaces, part II Jian Song 11:00 AM - 12:00 PM Uniformization of complete non-compact Kaehler manifolds and the Kaehler Ricci flow, part II Albert Chau