Fri, April 26, 2019
Public Access Category: All |
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- Time:
- 9:00am-10:15am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 9.00 am - 10.15 am.
Speaker: R.V. Gurjar.
Title: Linquan Ma’s generalisations of Lech’s Conjecture
Abstract: The following two results will be considered. Let (A,M) ⊂ (R,N) be a local flat homomorphism with A a regular local ring such that A contains its residue field. Let I be an ideal in A. Then eR/IR ≥ eR, where e denotes the multiplicity. Ma has stated four conjectures related to Lech’s Conjecture. We will discuss the relationships between these conjectures. If time permits, I will indicate how we can understand C.P. Ramanujam’s geometric interpretation of multiplicity in a more intuitive manner.
- Time:
- 10:15am-11:30am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time:10.15 am - 11.30 am.
Speaker: Sudeshna Roy
Title: Linquan Ma’s solution of the cyclic generalised Lech’s conjecture for graded rings
Abstract: Let R be a standard graded K-algebra and I be a homogeneous ideal. In this talk we show that if pdRR/I < ∞, then eR | eR/I. In particular, eR ≤ eR/I.
- Time:
- 11:45am-1:00pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 11.45 am - 01.00 pm.
Speaker: Kriti Goel.
Title: Numerically Robert rings.
- Time:
- 2:30pm-3:45pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 02.30 pm - 03.45 pm.
Speaker: Mitra Koley.
Title: Lech’s conjecture for 3-dimensional Gorenstein rings
Abstract for (3) and (4): Ma formulated a weakened generalised Lech’s conjecture and proved it for a class of rings known as numerically Roberts rings, in equal characteristic p > 0. Using these results, combined with results on Hilbert-Kunz multiplicities, he proved the Lech’s conjecture for 3-dimensional Gorenstein rings of equal characteristic p > 0. In the first part of the talk, we define numerically Roberts rings and prove a few results required for proving the main result, which will be proved in the second part of the talk.
- Time:
- 4:00pm-5:15pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 4.00 pm - 5.15 pm.
Speaker: Shreedevi Masuti.
Title: The Stru¨ckrad-Vogel conjecture
Abstract: Let M be a finite module of dimension d over a Noetherian local ring (R,m). The set{`(M/IM)/e(I,M)}, where I varies over m-primary ideals, is bounded below by (1/d!)e(R/textannM). If ˆ M is equidimensional, this set is bounded above by a constant depending only on M. The lower bound extends an inequality of Lech and the upper bound answers a question of Stru¨ckrad-Vogel.