July 13, 2020 - July 17, 2020
Public Access Category: All |
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- Time:
- 4:00pm-5:30pm
- Description:
- Lecture 2: Monday July 13th, 2020, from 4 pm to 5:30 pm
Title: The Narasimhan-Seshadri Theorem and Moduli spaces.
Google Meet Link: https://meet.google.com/xjq-pigk-bwo
Abstract: This will be an introduction to the Narasimhan-Seshadri Theorem
(1965) and its proof. I will make use of some later developments in
algebraic geometry (involving deformation theory, GIT-based moduli, and
algebraic spaces) not available in 1965, to simplify the exposition.
- Time:
- 6:30pm
- Description:
- Speaker: Dr. Tushar Bag, IIT Patna.
Time: 6:30 pm (gate opens 6:15 pm), 15 July, Wednesday.
Google Meet link: meet.google.com/aoz-gdsp-szk.
Phone: (US) +1 678-667-1924 PIN: 997 745 256#.
Title: Quantum Codes via Skew Cyclic Codes.
Abstract: In this presentation, we show a construction of quantum codes
from skew cyclic codes. Also, we discuss the advantages in the
construction of quantum codes from skew cyclic codes than from cyclic
codes over. Skew cyclic codes are equivalent to cyclic codes in the
commutative set up of linear codes. We derive a necessary and sufficient
condition for a skew cyclic code to contain its dual. Using this
dual-containing property, we show a construction of quantum codes from
them. We also present the usefulness of considering skew polynomial rings,
where we illustrate that, being non-unique factorization domains, skew
polynomial rings have numerous options for factors. As a result, we get
more options to construct codes with better parameters.
- Time:
- 5:30pm-6:30pm
- Description:
- Date and Time: 17 July 2020, 5:30 pm IST - 6:30 pm IST (joining time :
5:15 pm IST - 5:30 pm IST)
Google Meet Link: https://meet.google.com/gkc-hydx-fkn
Speaker: Dale Cutkosky, University of Missouri
Title: Mixed multiplicities and the Minkowski inequality for filtrations -
Part 2.
Abstract: We discuss the theory of multiplicities and mixed multiplicities
of filtrations of m-primary ideals. We show that many classical formulas
are true in this setting. We also consider the case of equality in
Minkowski's inequality. We give some general theorems characterizing when
this condition hold, giving generalizations of classical theorems of Rees,
Sharp, Teissier, Katz and others.