February 19, 2018 - February 23, 2018
Public Access Category: All |
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- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Stochastic Modelling and Simulation of Neuronal System with
Distributed Delay
Speaker: Prof. Karmeshu, JNU, Delhi
Day & Date: Monday, 19th February 2018
Time: 2.30 pm
Venue: Ramanujan Hall
Brief Bio: Professor Karmeshu has been with the School of Computer and
Systems
Sciences (SC&SS) at the Jawaharlal Nehru University, New Delhi since 1986.
He is
a recipient of the Shanti Swarup Bhatnagar Award in Mathematical Sciences
for the
year 1993, a Fellow of the National Academy of Sciences (India) and several
other
organisations. His primary research interests are in Mathematical Modelling
and
Computer Simulation.
Abstract: Modelling of neuronal dynamics aims to capture the mechanisms
that generate empirically observed
inter-spike interval (ISI) patterns. The time-interval between spikes gives
ISI distribution which requires
solution of the first passage time problem of the stochastic differential
equation governing the dynamics
of membrane potential when it reaches the threshold for the first time. The
empirical spiking patterns
exhibit both unimodal and bimodal/multimodal patterns. A theoretical model
based on generalized
neuronal model with distributed delay (GNMDD) is proposed to generate
multimodal/ bimodal inter
spike interval (ISI) distribution. Further the effect of external damped
oscillatory current in neuronal
model is investigated. It is found that with increasing amplitude of damped
oscillatory current, the
multimodal ISI distribution changes to unimodal ISI distribution when the
magnitude of external current
reaches some critical value. It is noted that the entropy also shows a
sudden transition around the
critical point. This phenomenon is akin to phase transition. This work is
done jointly with Sudheer
Sharma and Sanjeev Yadav.
- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG (Combinatorial Aspects of Commutative Algebra and Algebraic
Geometry) seminar
Speaker: Ronnie Sebastian
Date & Time : 19th February, 3:30pm
Venue : Ramanujan Hall
Abstract: This talk will be based on the following elementary and nice
exposition
http://www.math.stonybrook.edu/~roblaz/Reprints/Green.
Laz.Simple.Pf.Petri.pdf
Using some simple facts about projective space, cohomology, cohomology of
line bundles on projective space, we shall prove the following theorems:
1. Noether's theorem - Projective normality of the canonical embedding of
non-hyperelliptic curves.
2. Petri's -theorem - Let X be a smooth and projective curve of genus g
\geq 5. Assume that X carries a line bundle A of degree g-1 with h^0(A)=2.
Further assume that both A and \Omega_X\otimes A^* are generated by their
global sections. Then the homogeneous ideal of X in its canonical embedding
is generated by degree 2 elements.
- Time:
- 11:45am
- Location:
- Room No 215, Department of Mathematics
- Description:
- Commutative algebra seminar
Speaker: Madhusudan Manjunath
Date and time : Tuesday 20 Feb, 11.30am-1.00pm
Venue: Room 215
Title: Groebner bases of Toric Ideals.
Abstract: This is the first of two lectures where we'll cover Groebner
bases of toric ideals. We start with an introduction to toric ideals and
then study their Grobener bases. Our main goal will be a theorem of Bernd
Sturmfels from 1991 that relates (certain) initial ideals of toric ideals
to regular triangulations of an associated point configuration. The
lectures are based on Chapters 4 and 8 of the book ``Groebner Bases and
Convex Polytopes'' by Sturmfels.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Department Colloquium
Speaker: CS Dalawat, Harish Chandra research Institute
Date & Time: Tuesday, February 20, 2018, 16:00-17:00.
Venue: Ramanujan Hall
Title : Some footnotes to Galois's memoirs
Abstract : In his first memoir, Galois gave a criterion for an irreducible
equation of prime degree to be solvable by radicals. In the second memoir,
he defined primitive equations and showed that if a primitive equation is
solvable by radicals, then its degree is the power of a prime. His results
can be reformulated in terms of extensions of fields. We will show how to
extend this reformulation and parametrise all primitive solvable extensions
of an arbitrary field. (An extension is called primitive if there are no
intermediate extensions, and it is called solvable if the Galois group of
its Galois closure is a solvable group). All these concepts will be
recalled and illustrated through examples. If time permits, we will
discuss an arithmetic application. The talk should be accessible to a wide
audience, including students.
- Time:
- 1:45pm-2:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- POPULAR LECTURE
Date and Time: 21st February, Wednesday
1.45-2.45pm
Title:The Cartan-Dieudonne' Theorem
Speaker: Prof.J.K.Verma
Venue: Ramanujan Hall
Abstract: We shall discuss the Cartan-Dieudonne theorem which
establishes that every orthogonal transformation of the n-dimensional
Euclidean space is a composition of at most n reflections. We shall
show how to construct these n reflections using the Householder
matrices.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Mikhail Borovoi, Tel Aviv University, currently at TIFR
Date: Thursday, February 22, 2018
Time: 4:00 pm -- 5:00 pm
Venue: Ramanujan Hall
Title: Cayley groups
Abstract
:
I will start the talk from the classical "Cayley transform" for the special
orthogonal group SO(n) defined by Arthur Cayley in 1846. A connected linear
algebraic group G over C is called a *Cayley group* if it admits a *Cayley
map*, that is, a G-equivariant birational isomorphism between the group
variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley
group. A linear algebraic group G is called *stably Cayley* if G x S is
Cayley for some torus S. I will consider semisimple algebraic groups, in
particular, simple algebraic groups. I will describe classification of
Cayley simple groups and of stably Cayley semisimple groups. (Based on
joint works with Boris Kunyavskii and others.)