May 2018
Public Access Category: All
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4pm» Mathematics Colloquium- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Groups with norms: a PolyMath adventure
Speaker: Apoorva Khare (Indian Institute of Science)
Abstract:
Consider the following three properties of a general group G:
(1) Algebra: G is abelian and torsion-free.
(2) Analysis: G is a metric space that admits a "norm", namely, a
translation-invariant metric d(.,.) satisfying: d(1,g^n) = |n| d(1,g) for
all g in G and integers n.
(3) Geometry: G admits a length function with "saturated" subadditivity
for equal arguments: l(g^2) = 2 l(g) for all g in G.
While these properties may a priori seem different, in fact they turn out
to be equivalent. The nontrivial implication amounts to saying that there
does not exist a non-abelian group with a "norm".
We will discuss motivations from analysis, probability, and geometry; then
the proof of the above equivalences; and finally, the logistics of how the
problem was solved, via a PolyMath project
http://michaelnielsen.org/polymath1/index.php?title=Linear_norm
that began on a
blogpost https://terrytao.wordpress.com/2017/12/16/bi-invariant-metrics-of-linear-growth-on-the-free-group/
of Terence Tao.
(Joint - as D.H.J. PolyMath - with Tobias Fritz, Siddhartha Gadgil, Pace
Nielsen, Lior Silberman, and Terence Tao.)
- Time:
- 2:00pm - 3:00pm
- Location:
- Room No. 216, Department of Mathematics
- Description:
- Title of the talk- The Pick--Nevanlinna interpolation problem:
complex-analytic methods in special domains
Speaker- Vikramjeet Singh Chandel (post-doc candidate)
Abstract- attached
Time: 2 to 3 pm, May 24
Venue: Room 216
- Time:
- 3:00pm - 4:00pm
- Location:
- Room No. 216, Department of Mathematics
- Description:
- A talk under Analysis Seminar is scheduled as follows:
Title of the talk- Positive linear maps on matrix algebras and applications
Speaker- Hiroyuki Osaka
Abstract- attached
Time: 3 to 4 pm May 31, Thursday
Venue: Room 216