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DTSTART;TZID=America/New_York:20211001T093000
DTEND;TZID=America/New_York:20211001T103000
DTSTAMP:20260711T152315
CREATED:20240214T074545Z
LAST-MODIFIED:20240301T111944Z
UID:10002569-1633080600-1633084200@cmsa.fas.harvard.edu
SUMMARY:Instability of naked singularities in general relativity
DESCRIPTION:Member Seminar \nSpeaker: Jue Liu \nTitle: Instability of naked singularities in general relativity \nAbstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture\, proposed by Penrose\, which roughly states that for generic physical spacetime\, the singularities (if existed) must be hidden behind the black holes. Unfortunately\, the singularities visible to faraway observers\, which are called by naked singularities\, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime\, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases\, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method\, and it is this wild method that helps us to extend some results to the asymmetric cases.
URL:https://cmsa.fas.harvard.edu/event/10-1-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211008T093000
DTEND;TZID=America/New_York:20211008T103000
DTSTAMP:20260711T152315
CREATED:20240214T074201Z
LAST-MODIFIED:20240301T111834Z
UID:10002568-1633685400-1633689000@cmsa.fas.harvard.edu
SUMMARY:Knowledge Graph Embeddings and Inference
DESCRIPTION:Member Seminar \nSpeaker: Michael Douglas \nTitle: Knowledge Graph Embeddings and Inference \nAbstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data.\nA popular KG representation method is graph embedding\, which facilitates question answering\, inferring missing edges\, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning\, network learning\, and unstructured statistical inference\, and describe experiments to measure the contributions of each mechanism. \nJoint work with M. Simkin\, O. Ben-Eliezer\, T. Wu\, S. P. Chin\, T. V. Dang and A. Wood.
URL:https://cmsa.fas.harvard.edu/event/10-8-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211015T093000
DTEND;TZID=America/New_York:20211015T103000
DTSTAMP:20260711T152315
CREATED:20240214T073928Z
LAST-MODIFIED:20240301T111732Z
UID:10002566-1634290200-1634293800@cmsa.fas.harvard.edu
SUMMARY:C-P-T Fractionalization\, and Quantum Criticality Beyond the Standard Model
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: C-P-T Fractionalization\, and Quantum Criticality Beyond the Standard Model \nAbstract: Discrete spacetime symmetries of parity P or reflection R\, and time-reversal T\, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F\, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures\, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT)\, or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320. \nIn the second part of my talk\, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition\, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.
URL:https://cmsa.fas.harvard.edu/event/10-15-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211022T093000
DTEND;TZID=America/New_York:20211022T103000
DTSTAMP:20260711T152315
CREATED:20240214T073722Z
LAST-MODIFIED:20240301T111559Z
UID:10002564-1634895000-1634898600@cmsa.fas.harvard.edu
SUMMARY:Wall-crossing from Higgs bundles to vortices
DESCRIPTION:Speaker: Du Pei \nTitle: Wall-crossing from Higgs bundles to vortices \nAbstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk\, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.
URL:https://cmsa.fas.harvard.edu/event/10-22-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T093000
DTEND;TZID=America/New_York:20211029T103000
DTSTAMP:20260711T152315
CREATED:20240214T073521Z
LAST-MODIFIED:20240301T111455Z
UID:10002563-1635499800-1635503400@cmsa.fas.harvard.edu
SUMMARY:The complex Monge-Ampere equation in K\”ahler geometry
DESCRIPTION:Speaker: Freid Tong \nTitle: The complex Monge-Ampere equation in Kahler geometry \nAbstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry\, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk\, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry\, with a particular focus on the a priori C^0 estimates and their various applications. In the end\, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations\, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
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