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[3:30pm] R.V. Gurjar
 Description:
 Commutative Algebra seminar.
Speaker: R V Gurjar.
Affiliation: IIT Bombay.
Date and Time: Monday 19 August, 3:30 pm  5:00 pm.
Venue: Room 215, Department of Mathematics.
Title: Ramification in Commutative Algebra and Algebraic Geometry.
Abstract: We will consider mainly the following situation. Let R,S be
complete normal local domains over an alg. closed field k of char. 0 such
that S is integral over R. Our aim is to describe three ideals in S; I_N,
I_D, I_K (Noether, Dedekind, Kahler differents resp.) each of which
capture the ramified prime ideals in S over R. In general these three
ideals are not equal. An important special case when all are equal is when
S is flat over R. We will prove many of these statements.
The case when there is a finite group G of kautomorphisms of S such that
R is the ring of invariants is already very interesting. Then many nice
results are proved.
These include works of AuslanderBuchsbaum, ChevalleyShephardTodd,
Balwant Singh, L. Avramov, P. Roberts, P. Griffith, P. Samuel,....
I will try to discuss all these results.
I believe that these results and ideas involved in them will be very
valuable to students and faculty both.
Prerequisites. Basic knowledge of Commutative Algebra and language of
Algebraic Geometry (no sheaf theory!). I will
[4:00pm] Karthik Adimurthi : TIFR CAM, Bangalore: Mathematics Colloquium
 Description:
 Mathematics Colloquium
Speaker: Karthik Adimurthi.
Affiliation: TIFR CAM, Bangalore.
Date and Time: Monday 19 August, 4:00 pm  5:00 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Uniform boundedness and Lipschitz estimates for quasilinear
parabolic equations.
Abstract: In this talk, we will discuss some well known regularity issues
concerning equations of the form $u_t  div \nabla u^{p2} \nabla u = 0$
for $1
2$) and the singular case ($p<2$)
separately. Moreover in several instances, the estimates are not even
stable as $p\rightarrow 2$. In this talk, I shall discuss two regularity
estimates and give an overview on how to obtain uniform $L^{\infty}$ and
$C^{0,1}$ estimates in the full range $\frac{2N}{N+2}


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