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  1. Fellowship of the Ring, National Seminar: The dual graph of a ring

    Location: MSRI: Online/Virtual
    Speakers: Matteo Varbaro (Università di Genova)

    To attend this seminar, you must register in advance, by clicking HERE.

    The dual graph (a.k.a. Hochster-Huneke graph) G(R) of a Noetherian ring R of dimension d is the finite simple graph whose vertices correspond to the minimal primes of R and such that {P,Q} is an edge iff R/(P+Q) has dimension d-1.
    After showing some basic properties, we will discuss three fundamental results of Grothendieck, Hartshorne, and Hochster-Huneke, concerning the connectedness of G(R). We will also see, given a finite simple graph G, how to construct a Noetherian ring R such that G(R)=R.

    In the second part of the talk, we will discuss some recent developments related to the following two questions:
    1) How many paths are there between two minimal primes of R?
    2) What is the shortest path between two minimal primes of R?
    By taking the minimum in 1) and the maximum in 2) varying the pair of minimal primes we get two important invariants of the graph G(R): its vertex connectivity and its diameter. Most of the things that I will discuss are contained in works written together with Bruno Benedetti, Barbara Bolognese and Michela Di Marca.

    Updated on May 22, 2020 08:45 AM PDT
  2. Fellowship of the Ring, National Seminar: A truly mutually beneficial friendship: how Stanley-Reisner theory enhanced both combinatorics and algebra

    Location: MSRI: Online/Virtual
    Speakers: Hailong Dao (University of Kansas)

    To attend this seminar, you must register in advance, by clicking HERE.

    Given a simplicial complex on n vertices, one can associate to it a quotient of the polynomial ring in n variables, called the Stanley-Reisner ring. Starting with the proof of the Upper Bound Conjecture for spheres, this approach has been spectacularly useful in bringing tools from commutative algebra to the study of simplicial complexes. In the first part of the talk I will sketch some relevant parts of this story. In the second, I will describe how modern tools, including cohomological vanishing results and characteristic p methods, have inspired new developments. At the same time, results obtained on the combinatorics side now can be brought back to induce interesting new questions and theorems on the algebra side. One thing I really like about this topic is that it can be used to generate good problems at all levels, including for high school students.

    Updated on May 11, 2020 04:24 PM PDT
  1. 2020 African Diaspora Joint Mathematics Workshop

    The African Diaspora Joint Mathematics Workshop (ADJOINT) will take place at the Mathematical Sciences Research Institute in Berkeley, CA from June 15 to June 26, 2020.

    ADJOINT is a two-week summer activity designed for researchers with a Ph.D. degree in the mathematical sciences who are interested in conducting research in a collegial environment.  

    The main objective of ADJOINT is to provide opportunities for in-person research collaboration to U.S. mathematicians, especially those from the African Diaspora, who will work in small groups with research leaders on various research projects. 

    Through this effort, MSRI aims to establish and promote research communities that will foster and strengthen research productivity and career development among its participants. The ADJOINT workshops are designed to catalyze research collaborations, provide support for conferences to increase the visibility of the researchers, and to develop a sense of community among the mathematicians who attend. 

    The end goal of this program is to enhance the mathematical sciences and its community by positively affecting the research and careers of African-American mathematicians and supporting their efforts to achieve full access and engagement in the broader research community. 

    During the workshop, each participant will: 

    • conduct research at MSRI within a group of four to five mathematicians under the direction of one of the research leaders 
    • participate in professional enhancement activities provided by the onsite ADJOINT Director 
    • receive funding for two weeks of lodging, meals and incidentals, and one round-trip travel to Berkeley, CA 

    After the two-week workshop, each participant will:

    • have the opportunity to further their research project with the team members including the research leader 
    • have access to funding to attend conference(s) or to meet with other team members to pursue the research project, or to present results 
    • become part of a network of research and career mentors

    Updated on Jun 04, 2020 12:01 PM PDT

Past Seminars

  1. Seminar Fellowship of the Ring, National Seminar: Commutative Algebra with S_n-invariant monomial ideals

    To attend this seminar, you must register in advance, by clicking HERE.

    Consider a polynomial ring in n variables, together with the action of the symmetric group by coordinate permutations. In my talk I will describe many familiar notions in Commutative Algebra in the context of monomial ideals that are preserved by the action of the symmetric group. These include Castelnuovo-Mumford regularity, projective dimension, saturation, symbolic powers, or the Cohen-Macaulay property. My goal is to explain how changing focus from minimal resolutions to Ext modules can lead to a simplified picture of the homological algebra, and to provide concrete combinatorial recipes to determine the relevant homological invariants.

    Updated on May 01, 2020 12:25 PM PDT
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.