Aug-Nov 2024 | Jan-Apr 2024 | Jan-Apr 2020 | Aug-Nov 2019

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Aug-Nov 2024

• Monday, 2024-Aug-26, 15:30-16:30, Room TBD
  • Speaker: Manoj Kummini
  • Title: Maximal Cohen-Macaulay modules
  • Abstract: This semester we will work through the book of Buchweitz, Maximal Cohen-Macaulay Modules and Tate Cohomology, AMS.

Jan-Apr 2024

• Monday, 2024-Apr-15, 14:00-15:00, Room LH-1
  • Speaker: Kanoy Das
  • Title: Castelnuovo-Mumford regularity of symbolic powers of ideals
  • Abstract: We discuss an alternative proof of the celebrated result of J. Herzog, T. Hibi, and N. V. Trung about the asymptotic behaviour of Castelnuovo-Mumford regularity of symbolic powers of monomial ideals due to L. T. Hoa, and T. N. Trung.
• Tuesday, 2024-Apr-09, 15:40-16:40, Room LH-1
  • Speaker: Nirmal Kotal
  • Title: Frobenius-Betti numbers (cont.)
• Tuesday, 2024-Apr-02, 15:40-16:40, Room LH-1
  • Speaker: Nirmal Kotal
  • Title: Frobenius-Betti numbers (cont.)
• Tuesday, 2024-Mar-26, 15:40-16:40, Room LH-1
  • Speaker: Nirmal Kotal
  • Title: Frobenius-Betti numbers
• Tuesday, 2024-Mar-12, 15:40-16:40, Room LH-1
  • Speaker: Manoj Kummini
  • Title: Local cohomology and group actions (cont.)
  • Abstract: see below.
• Tuesday, 2024-Mar-05, 15:40-16:40, Room LH-1
  • Speaker: Manoj Kummini
  • Title: Local cohomology and group actions (cont.)
  • Abstract: see below.
• Tuesday, 2024-Feb-27, 15:40-16:40, Room LH-1
  • Speaker: Manoj Kummini
  • Title: Local cohomology and group actions (cont.)
  • Abstract: see below.
• Tuesday, 2024-Feb-20, 15:40-16:40, Room LH-1
  • Speaker: Manoj Kummini
  • Title: Local cohomology and group actions.
  • Abstract: Lecture 1: introduction to local cohomology; Lecture 2–3: discussion of the paper Symonds, Group actions on rings and the Cech complex, Adv. Math., 2013.

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Jan-Apr 2020

• Postponed
• Thursday, 2020-Mar-12, 15:30-16:45, Room LH-4
  • Speaker: Neelarnab Raha, CMI
  • Title: Test ideals for Gorenstein rings (continued.)
  • Speaker: Nirmal Kotal, CMI
  • Title: Briancon-Skoda theorem, using tight closure
• Thursday, 2020-Mar-05, 15:30-16:45, Room LH-4
  • Speaker: Neelarnab Raha, CMI
  • Title: Test ideals for Gorenstein rings (continued.)
• Thursday, 2020-Feb-27, 15:30-16:45, Room LH-4 : No talk
• Thursday, 2020-Feb-27, 15:30-16:45, Room LH-4
  • Speaker: Neelarnab Raha, CMI
  • Title: Test ideals for Gorenstein rings (continued.)
• Thursday, 2020-Feb-20, 15:30-16:45, Room LH-4
  • Speaker: Neelarnab Raha, CMI
  • Title: Test ideals for Gorenstein rings
• Thursday, 2020-Feb-13, 15:30-16:45, Room LH-4
  • Speaker: Nirmal Kotal, CMI
  • Title: Test ideals (continued.)
• Thursday, 2020-Feb-06, 15:30-16:45, Room LH-4
  • Speaker: Nirmal Kotal, CMI
  • Title: Test ideals (continued.)
• Thursday, 2020-Jan-30, 15:30-16:45, Room LH-4
  • Speaker: Nirmal Kotal, CMI
  • Title: Test elements and test ideals: definition and basic properties
• Thursday, 2020-Jan-23, 15:30-16:45, Room LH-4
  • Speaker: Dharm Veer, CMI
  • Title: Fedder's criterion
• Thursday, 2020-Jan-16, 15:30-16:45, Room LH-4
  • Speaker: Dharm Veer, CMI
  • Title: F-pure and F-split rings
• Thursday, 2020-Jan-09, 15:30-16:45, Room LH-4
  • Speaker: Dharm Veer, CMI
  • Title: Flatness of the Frobenius endomorphism

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Aug-Nov 2019

These are listed reverse-chonologically.

• Monday, 2019-Nov-18, 15:45-16:45, Room LH-6
  • Speaker: Dharm Veer, CMI
  • Title: Tate resolutions (continued.)
• Thursday, 2019-Nov-14, 15:30-17:00, Room LH-1
  • Speaker: Dharm Veer, CMI
  • Title: Tate resolutions
  • Abstract: Following Tate's paper 'Homology of noetherian rings and local rings (1957)' we will look at skew-commutative differential graded algebras (Such an algebra is called an R-algebra) over a commutative noetherian ring R. We will first show that there always exists a free resolution X of the residue class ring R/I which is an R-algebra and we will use these resolutions to study the algebra structure of Tor^R(R/I,R/J).
• Thursday, 2019-Oct-24, 15:30-17:00, Room LH-1
  • Speaker: Kumari Saloni, CMI
  • Title: Koszul algebras (continued.)
• Thursday, 2019-Oct-17, 15:30-17:00, Room LH-1
  • Speaker: Kumari Saloni, CMI
  • Title: Koszul algebras (continued.)
• Thursday, 2019-Oct-10, 15:30-17:00, Room LH-1
  • Speaker: Kumari Saloni, CMI
  • Title: Koszul algebras
  • Abstract: Koszul algebra is a graded K-algebra R whose residue field K has a linear free resolution as an R-module. From certain point of views, Koszul algebras behave homologically as polynomial rings. To check that an algebra is Koszul is usually a difficult task. We will discuss some methods in this direction.
• Thursday, 2019-Sep-12, 15:30-17:00, Room LH-1
  • Speaker: Aditya Subramaniam, CMI
  • Title: Newton-Okounkov bodies (continued.)
• Thursday, 2019-Sep-05, 15:30-17:00, Room LH-1
  • Speaker: Aditya Subramaniam, CMI
  • Title: Newton-Okounkov bodies (continued.)
• Wednesday, 2019-Sep-04, 15:30-17:00, Room LH-1
  • Speaker: Aditya Subramaniam, CMI
  • Title: Newton-Okounkov bodies (continued.)
• Thursday, 2019-Aug-29, postponed to 2019-Sep-04
• Thursday, 2019-Aug-22, 15:30-17:00, Room LH-1
  • Speaker: Aditya Subramaniam, CMI
  • Title: Newton-Okounkov bodies (continued.)
• Thursday, 2019-Aug-08, 15:30-17:00, Room LH-1
  • Speaker: Aditya Subramaniam, CMI
  • Title: Newton-Okounkov bodies (continued.)
• Thursday, 2019-Aug-01, 15:30-17:00, Room 801
  • Speaker: Aditya Subramaniam, CMI
  • Title: Newton-Okounkov bodies
  • Abstract: The theory of Newton-Okounkov bodies, also called as Okounkov bodies, is a new connection between algebraic geometry and convex geometry. Okounkov bodies were first introduced by Andrei Okounkov, in a construction motivated by a question of Khovanskii concerning convex bodies governing multiplicities of representations. Kaveh-Khovanskii and Lazarsfeld-Mustata have generalized and systematically developed Okounkov's construction, showing the existence of convex bodies which capture much of the asymptotic information about the geometry of (X, D) where X is an algebraic variety and D is a big divisor. The main goal of these lectures is to understand Okounkov's construction given by Lazarsfeld-Mustata and give applications to Seshadri Constants. References:
    1. Robert Lazarsfeld and Mircea Mustata, Convex bodies associated to linear series, Ann. Sci. Ec. Norm.Super.(4) 42 (2009), no.5, 783-835.
    2. Kiumars Kaveh and A.G. Khovanskii, Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, Ann. of Math (2)176 (2012), no.2, 925-978.
    3. Alex Kuronya and Victor Lozovanu, Geometric aspects of Newton-Okounkov Bodies, Phenomenological approach to algebraic geometry, 137-212, Banach Center Publ.,116, Polish Acad. Sci. Inst. Math., Warsaw,2018.