Theoretical Statistics and Mathematics Unit

## Past month's Seminars and Colloquia

[Past seminars of this year] [Colloquia archive] [All Seminars archive]

### COLLOQUIUM

Title :Non-commutative Twisted Euler characteristic in Iwasawa theory
Speaker : Sudhanshu Shekhar (IIT Kanpur)
Time : October 26, 2017 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : It is well known that given a finitely generated torsion module $M$ over the Iwasawa algebra $\Z_p[[\Gamma ]]:= \varprojlim_n \ZZ_p[\Gamma/ \Gamma^{p^n}]$, where $\Gamma \cong \Z_p$, there exists a continuous $p$-adic character $\rho$ of $\Gamma$ such that, for the twist $M(\rho):=M\otimes_{\ZZ_p} \rho$ of $M$, the $\Gamma_n : = \Gamma^{p^n}$ Euler characteristic is finite for every $n$. We prove a generalization of this result by considering modules over the Iwasawa algebra of a general $p$-adic Lie group $G$, instead of $\Gamma$. This is a joint work with Somnath Jha.

### STUDENT SEMINAR

Title : Translational tilings of the plane
Speaker : Siddartha Bhattacharya (TIFR Mumbai)
Time : October 31, 2017 (Tuesday), 03:15 PM
Venue : Auditorium
Abstract : For $d\ge 1$, a set $A\subset {\mathbb R}^d$ tiles ${\mathbb R}^d$ if ${\mathbb R}^d$ can be expressed as a disjoint union of translates of $A$. In this talk we will discuss the connection between these tilings and dynamical systems. In particular, we will show that in the $d = 2$ case the tiling problem is decidable for a large class of sets.

### STUDENT SEMINAR

Title : Modelling and research gaps in inclusive innovation research
Speaker : Anil Gupta (IIM Ahmedabad and Founder of Honey Bee network)
Time : November 7, 2017 (Tuesday), 02:00 PM
Venue : Auditorium

### COLLOQUIUM

Title :Multiplicity theorem of singular Spectrum for general Anderson type Hamiltonian
Speaker : Anish Mallick (ICTS-TIFR Bangalore)
Time : November 9, 2017 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : Random operators are an important field of study because of their role in the theory of disordered media. One of the early models that used randomness is the Anderson tight binding model, which was developed to study spin wave diffusion in doped semiconductors. To study the random operator is same as understanding the spectrum of the operator, and part of the spectral theorem deals with multiplicity of the operator. In case of Anderson type operator there are many results identifying pure point spectrum and in some cases singular continuous and absolutely continuous spectrum, but except for Anderson tight binding model multiplicity of spectrum is unknown. Here we focus on the multiplicity problem for Anderson type random operators and provide bound on multiplicity of singular spectrum using the Green's function associated with each of the perturbation (disorder is viewed as series of perturbation). In general these type of result are false for fixed operator and these analysis works because of disorder. Using the conclusions obtained, simplicity and bound on multiplicity is also obtained for certain family of random operators.

### COLLOQUIUM

Title :A complete class of Type 1 optimal block designs with unequal replications
Speaker : Sunanda Bagchi (ISI Bangalore)
Time : November 16, 2017 (Thursday), 03:15 PM
Venue : Auditorium
Abstract : Consider a class $\Phi$ of optimality criteria. Suppose ${\cal D}^*$ is a subclass of ${\cal D}$, a class of block designs, such that every member of ${\cal D} \setminus {\cal D}^*$ is worse than a member of ${\cal D}^*$, with respect to every criterion in $\Phi$. Then, we say that ${\cal D}^*$ is a complete class w.r.t. $\Phi$. We consider the set up where $bk = vr +1$ and $r(k-1)/(v-1)$ is an odd integer. We take ${\cal D}$ to be the class of all connected block designs with $b$ blocks of size $k$ each and $v$ treatments and $\Phi$ to be the class of all Type 1 criteria [Cheng(1978)]. In the case $k =5$, we have obtained a complete class ${\cal D}^*$ of size $4$ in ${\cal D}$ with respect to $\Phi$. The designs in ${\cal D}^*$ are linearly ordered in terms of A-optimality. Further, designs in ${\cal D}^*$ have been constructed for a few small values of $v$. We conjecture that a complete class of size at most $k-1$ w.r.t. $\Phi$ exists for the same set up with any odd $k$.

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