UCSD Differential Geometry Seminar
UCSD Differential Geometry Seminar |
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Wednesday October 20, 2010.
Room and Time: AP&M 5829, 4-5pm.
Title: Short-time existence of the Ricci flow on noncompact Riemannian manifolds
Abstract: In this talk, using the local Ricci flow, we prove the
short-time existence of the Ricci flow on noncompact manifolds, whose
Ricci curvature has global lower bound and sectional curvature has only
local average integral bound. The short-time existence of the Ricci
flow on noncompact manifolds was studied by Wan-Xiong Shi in 1990s, who
required a point-wise bound of curvature tensors. As a corollary of our
main theorem, we get the short-time existence part of Shi's theorem in
this more general context.
Wednesday October 27, 2010.
Room and Time: Room 5829, 4-5pm.
Speaker: Yuguang Zhang, Capital Normal University, Beijing
Title: Continuity of Conifold Transitions and Flops for Calabi-Yau Manifolds
Abstract: In this talk, we present a proof of a weaker version
of the Candelas de la Ossa's conjecture, i.e. conifold transitions and
flops for Ricci-flat Calabi-Yau manifolds are continuous in the
Gromov-Hausdorff sense.
Tuesday November 2, 2010.
**** JOINT UCI-UCSD DIFFERENTIAL GEOMETRY SEMINAR ****
**** HELD AT UC IRVINE, ROWLAND HALL ****
Room and Time: UCI Rowland Hall 340P, 3-4pm.
Speaker: David Glickenstein, University of Arizona
Title: Discrete conformal variations and discrete scalar
curvature
Room and Time: UCI Rowland Hall 306, 4-5pm.
Speaker: Peng Lu, University of Oregon
Title: Local Curvature Bound in Ricci Flow
For more details on these talks, see: UCI
Seminar Schedule
Wednesday November 3, 2010.
Room and Time: AP&M 6402, 4-5pm.
Speaker: Peter Petersen, UCLA.
Title: Warped Product Einstein Structures
Abstract: We will discuss old and new questions about when a
fixed Riemannian manifold is the base of a warped product Einstein
manifold. This problem has been completely solved when the base is 1 or
2-dimensional and much progress has been made in higher dimensions as
well. There are also many interesting extensions to the case where the
base might have boundary and when we allow for warping functions that
change sign.
Wednesday December 1, 2010.
Room and Time: AP&M 5829, 4-5pm.
Speaker: Diego Matessi, Universita del Piemonte Orientale.
Title: Conifold transitions via tropical geometry
Abstract: The process of degenerating a complex variety X to a
singular variety X_0
and then resolving to obtain X' is called a geometric transition. The case
where
the singularities are just double points is called a conifold transition.
There
are known obstructions to either resolving a set of nodes or smoothing
them, depending
on whether we want to preserve respectively the symplectic or complex
structure.
Moreover mirror symmetry is thought to reverse this process, i.e. the
mirror of a
smoothing is expected to be a resolution and vice versa. I will explain
an
interpretation
of these facts in terms of "tropical geometry", which encodes information
of both symplectic
and complex geometry in terms of discrete data.
Wednesday January 12, 2011.
Room and Time: Room AP&M 7421, 3-4pm.
Speaker: Pun Wai Tong, UCSD
Title: Singularity Theorems in Space-Time
Monday January 24, 2011.
Room and Time: Room AP&M 5829, 4-5pm.
Speaker: Robert Haslhofer, ETH Zurich
Title: Compactness of the shrinkers
Wednesday January 26, 2011.
Room and Time: Room AP&M 5829, 4-5pm.
Speaker: Tom Ilmanen, ETH Zurich
Title: Initial Time Singularities in Mean Curvature Flow
Abstract: Let M_0 be a closed subset of R^n+1 that is a smooth hypersurface except for a finite number of isolated singular points. Suppose that M_0 is asymptotic to a regular cone near each singular point.
Can we flow M_0 by mean curvature?
Theorem (n<7): there exists a smooth mean curvature evolution starting at M_0 and defined for a short time t less than epsilon.
Such an initial M_0 might arise as the limit of a smooth mean curvature evolution defined earlier than t=0. Thus, the result allows us to flow through singularities in some cases.
We use a monotonicity formula that complements the monotonicity
formula of Huisken. The method applies to other geometric heat flows
as well.
Friday February 25, 2011.
Room and Time: Room AP&M 6402, 3-4pm
Speaker: Xiangdong Li, Chinese Academy of Science
Title: Perelman's entropy for the
Witten Laplacian
on Riemannian
manifolds via the Bakry Emery
Ricci
curvature
Friday February 25, 2011.
Room and Time: Room AP&M 6402, 4-5pm
Speaker: Xiaodong Cao, Cornell
Title: Harnack Inequalities, Heat Kernel Estimates and the Ricci flow
Abstract: In this talk, we will discuss about Li-Yau-Hamilton
type differential
Harnack inequalities, heat kernel estimates and their applications to
study type I ancient solutions of the Ricci flow.
Saturday and Sunday February 26-27, 2011
*** THE 18TH SOUTHERN CALIFORNIA GEOMETRIC ANALYSIS SEMINAR ***
Held at UCSD in Center Hall 105.
Go to Conference Website for details and program.
Wednesday March 2, 2011.
Room and Time: Room AP&M 5829, 4-5pm
Speaker: Leobardo Rosales, Rice University
Title: Bernstein's Theorem for the two-valued minimal surface equation
Abstract: We explore the question of whether there are
nontrivial solutions to the two-valued minimal surface (2MSE) equation
defined over the punctured plane. The 2MSE is a non-uniformly elliptic
PDE, degenerate at the origin, originally introduced by N.Wickramasekera
and L.Simon to produce examples of stable branched minimal immersions.
Wednesday April 6th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Speaker: Ben Weinkove, UCSD
Title: [Informal Seminar] Convergence of Kahler-Ricci flow on Fano Manifolds
Abstract: This is an expository talk. I will discuss the recent
paper of Tian and Zhu on the Kahler-Ricci flow on Fano manifolds.
Tuesday April 12, 2011. JOINT UCI-UCSD DIFFERENTIAL GEOMETRY SEMINAR
HELD AT UC IRVINE.
Room and Time: 3pm, Rowland Hall 306 (UCI)
Speaker: Gabor
Szekelyhidi, Columbia
University.
Title: TBA
Room and Time: 4pm, Rowland Hall 306 (UCI)
Speaker: Maciej
Dunajski, University of
Cambridge.
Title: How to recognize a Kahler metric?
For more details, see the UC
Irvine Seminar Page
Wednesday April 13th, 2011.
Room and Time: Room 5402, 4-5pm
Speaker: Brett Kotschwar, Max Planck Institute for Gravitational Physics, Potsdam
Title: Ricci flow and the holonomy group
Abstract: I will discuss a "non-contraction" result for the
holonomy
group of a solution to Ricci flow, namely,
that if the reduced holonomy of a complete solution of uniformly
bounded curvature is restricted to a subgroup
of SO(n) at some non-initial time, it must be restricted to the same
subgroup at all previous times; it follows then
from existing results that the holonomy group is exactly preserved by
the equation. In particular, a solution
may be Kahler or locally reducible (as a product) on some time
slice only if it is identically so on its entire interval of
existence.
In contrast to the question of "non-expansion" of holonomy, the
problem of non-contraction cannot be reduced completely to
an application of the classification and splitting theorems of Berger
and De Rham and a series of appeals to a relevant uniqueness theorem
(here, backwards-uniqueness). However, with an infinitesimal
reformulation,
we show that the problem can nevertheless be reduced to one of unique
continuation, and specifically to one for a coupled system of partial-
and ordinary-differential inequalities of a form amenable to an
approach by Carleman inequalities. This reformulation also leads to an
alternative and essentially self-contained proof of the non-expansion
of holonomy via the analysis of a similar (albeit simpler and strictly
parabolic) system by means of the maximum principle.
Thursday April 14th, 2011.
Room and Time: Room 6218, 2-3pm
Speaker: Bennett Chow, UCSD
Title: [Informal Seminar] Introduction to gradient Ricci solitons
Abstract: Gradient Ricci solitons are those Riemannian
manifolds whose Ricci tensor
is equal to a constant multiple of the metric plus the hessian of a
function. I will discuss some aspects of the literature on complete
gradient Ricci solitons assuming that the hessian of the function is not
identically zero.
Wednesday April 20th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Speaker: Ben Weinkove, UCSD
Title: [Informal Seminar] Convergence of Kahler-Ricci flow on Fano Manifolds
Abstract: This is part two of an expository talk on the recent
paper of Tian and Zhu on the Kahler-Ricci flow on Fano manifolds.
Wednesday April 27th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Speaker: Bo Yang, UCSD
Title: Complete U(n) invariant Kahler metrics of positive curvature on C^n
Abstract: It is an expository talk of the recent work of Wu and
Zheng. Their work develop a systematic way to construct complete U(n)
invariant Kahler metrics of positive curvature on C^{n}. Studying the
geometry of those metrics should be interesting. I will mention a simple
application if time permits.
Thursday April 28th, 2011.
Room and Time: Room AP&M 6218, 2-3pm
Speaker: Bennett Chow, UCSD
Title: [Informal Seminar] Introduction to gradient Ricci solitons (Part II)
Abstract: Gradient Ricci solitons are those
Riemannian
manifolds whose Ricci tensor
is equal to a constant multiple of the metric plus the hessian of a
function. I will discuss some aspects of the literature on complete
gradient Ricci solitons assuming that the hessian of the function is not
identically zero.
Monday May 2, 2011.
Room and Time: Room AP&M 5829, 4-5pm
Speaker: Mauro Carfora, University of Pavia
Title: Ricci flow conjugation and Initial data sets for Einstein Equation
Abstract: We discuss a natural form of Ricci-Flow conjugation
between two
distinct general relativistic data sets given on a compact
n-dimensional manifold.
The Ricci flow generates a form of L^2 parabolic averaging, of one data
set with respect to the other, with a number of desiderable properties:
(i) Preservation of the dominant energy condition; (ii) Localization by a
heat kernel, (associated with the linearized Ricci flow), whose support
sets the scale of averaging; (iii) Entropic stability.
Wednesday May 4th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Speaker: Ben Weinkove, UCSD
Title: [Informal Seminar] The weak Kahler-Ricci flow
Abstract: This is an expository talk introducing the weak
Kahler-Ricci
flow.
Wednesday May 11th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Title: [Informatl Seminar] Gauss Curvature flow I
Wednesday May 18th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Title: [Informal Seminar] Gauss Curvature flow II
Wednesday May 25th, 2011.
Room and Time: Room AP&M 6218, 1-2pm
Speaker: Bennett Chow, UCSD
Title: Introduction to Gradient Ricci solitons (Part III)
Abstract: Gradient Ricci solitons are those Riemannian manifolds
whose Ricci tensor is equal to a constant multiple of the metric plus the
hessian of a function. I will discuss some aspects of the literature on
complete gradient Ricci solitons assuming that the hessian of the function
is not identically zero.
Wednesday May 25th, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Speaker: Matt Gill, UCSD
Title: Metric Flips with Calabi Ansatz
Abstract: We discuss a portion of the paper by Song and Yuan
titled "Metric Flips with Calabi Ansatz." In particular, they give an
example of where the Kahler-Ricci flow performs a flip as an analytic
analogue to Mori's minimal model program.
Wednesday June 1st, 2011.
Room and Time: Room AP&M 5402, 4-5pm
Speaker: Ben Weinkove, UCSD
Title: [Informal Seminar] The Kahler-Ricci flow on a smooth minimal model of general type
Abstract: This is an expository talk on the behavior of
the Kahler-Ricci flow on a smooth minimal model of general type. I will
show that the flow converges to a singular Kahler-Einstein metric.
Questions: Contact Ben Weinkove (weinkove@math) or Lei Ni (lni@math).
Email addresses end in ucsd.edu
See the 2009-2010 Differential Geometry Seminar schedule.
See the 2008-2009 Differential Geometry Seminar schedule.
Return to UCSD Mathematics homepage.