Organizer(s) | Xiaojun Huang, Jian Song, Sagun Chanillo, Hanlong Fang | Archive |
Upcoming Talks
Friday, April 28th |
Shan-Tai Chan , Syracuse University |
"On holomorphic isometries from the Poincar'e disk into bounded symmetric domains of rank at least two" |
Time: 10:30 AM |
Location: Hill 705 |
Abstract: In general, it is difficult to classify all holomorphic isometries from the unit disk into bounded symmetric domainsâ€‹ with respect to their Bergman metrics up to normalizing constants, especially when the target is of rank at least three. Thus, in this talk we will first consider holomorphic isometries from the Poincar'e disk into the product of the unit disk and the complex unit n-ball for n at least two with respect to certain canonical K"ahler metrics and obtain a complete characterization of all such holomorphic isometries. On the other hand, I will also talk about how our study would provide new examples of holomorphic isometries from the Poincar'e disk into irreducible bounded symmetric domains of rank at least 2 except for type-IV domains.
This is a joint work with Yuan Yuan. |
Past Talks
Friday, April 21st |
Song-Ying Li , UC Irvine |
"Rigidity theorems for invariant harmonic functions on bounded symmetric domains" |
Time: 10:30 AM |
Location: Hill 705 |
Abstract: Let $Delta_g$ be the Laplace-Beltrami operator in Bergman metric
in the unit ball in $C^n$. Then the boundary value problem:
$$ Delta_g u=0, hbox{ in } B_n; quad u=phi hbox{ on }d B_n $$ has a unique solution $$ u(z)=P[phi]=int_{d B_n} {(1-|z|^2)^n over |1-langle z, w angle|^{2n}} phi(w) dsigma(w) $$ It well known that even if $phiin C^infty(d B_n)$, $P[phi]$ may not be in $C^n(overline{B_n})$. A well known theorem of R. Graham says that if $u$ is invariant harmonic in $B_n$ and $C^n(overline{B_n})$, then $u$ must be pluriharmonic in $B_n$. In this talk, I will present a joint work with R-Y. Chen, we try to generalize Graham's theorem to the bounded symmetric domains. |
Friday, March 31st |
Sai-Kee Yeung, Purdue University |
"Hyperbolicity of some moduli spaces of polarized manifolds" |
Time: 2:00 PM |
Location: Hill 705 |
Abstract: In this talk, we would explain some joint work with Wing-Keung To on hyperbolicity of moduli spaces of polarized algebraic manifolds, including families or moduli spaces of Kaehler-Einstein manifolds of negative scalar curvature or trivial scalar curvature, and some log-general type manifolds for quasi-projective versions. Classically, results on moduli space of Riemann surfaces of genus at least two have been obtained by Ahlfors, Royden and Wolpert with Weil-Petersson metric. Study of moduli of higher dimensional manifolds in terms of Weil-Petersson metrics began with a work of Siu thirty years ago. Eventually, we construct a negatively curved Finsler metric on such moduli from which results in hyperbolicity follow naturally. We also apply the related techniques to study questions related to a conjecture of Viehweg. |
Friday, March 24th |
Special Complex Analysis and Geometry Seminar |
Yumeng Ou, MIT |
"Sparse domination of singular integral operators" |
Time: 10:30 AM |
Location: Hill 705 |
Abstract: It is discovered recently by Lacey (and refined by Lerner) that Calder'on-Zygmund (CZ) operators, which are a priori non-local, can be dominated pointwisely by a class of local, positive, sparse averaging operators. This in particular implies sharp weighted norm inequalities for CZ operators. In a series of joint works with A. Culiuc and F. Di Plinio, we show that sparse domination can be obtained in contexts well beyond CZ theory, such as for rough homogeneous singular integrals, Bochner-Riesz multipliers, and even modulation invariant multilinear singular integrals including the bilinear Hilbert transforms. Many new sharp weighted estimates for these operators then follow immediately. |
Friday, February 17th |
Andrew Zimmer , University of Chicago |
"Metric spaces of non-positive curvature and applications in several complex variables" |
Time: 10:30 AM |
Location: Hill 705 |
Abstract:
In this talk I will discuss how to use ideas from the theory of metric spaces of non-positive curvature to understand the behavior of holomorphic maps between bounded domains in complex Euclidean space. Every bounded domain has an metric, called the Kobayashi metric, which is distance non-increasing with respect to holomorphic maps. Moreover, this metric often satisfies well-known non-positive curvature type conditions (for instance, Gromov hyperbolicity or visibility) and one can then use these conditions to understand the behavior of holomorphic maps.
Some of what I will talk about is joint work with Gautam. |