Theoretical Statistics and Mathematics Unit | ||
Past month's Seminars and Colloquia |
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[Past seminars of this year] [Colloquia archive] [All Seminars archive] | ||
COLLOQUIUMTitle :Non-commutative Twisted Euler characteristic in Iwasawa theorySpeaker : 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 SEMINARTitle : Translational tilings of the planeSpeaker : 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 SEMINARTitle : Modelling and research gaps in inclusive innovation researchSpeaker : Anil Gupta (IIM Ahmedabad and Founder of Honey Bee network) Time : November 7, 2017 (Tuesday), 02:00 PM Venue : Auditorium Abstract : The inclusivity of any innovation depends upon the degree to which the solution is accessible, affordable, available and adaptable to disadvantaged communities. The disadvantages can arise on account of spatial, sectoral, social, skill, seasonal or temporal and structural (on account of ill designed governance system) exclusion of the people. Innovations are defined as new ways of addressing an unmet need through modification in one of the four dimensions of a product or service involving : material, method, applications/uses or delivery. At least one of the four should be new: a solution may have new material but used by an old method, for old purpose and even old or already existing delivery system and likewise fr other parameters. It is possible that one can have novelty in more than one parameters. These solutions can emerge from grassroots, for grassroots application by outsiders, with grassroots communities through collaborative design and delivery or at grassroots that is just located at community level without involving them in the innovation design process. The theory of social transformation requires modelling technological, institutional, and socio-cultural dimensions of resource use, community response and developmental outcomes. There are many assumptions which guide developmental change but one of the crucial sub-set of change is widening of decision making options and extending the time frame of decision making. Longer the timeframe, wider the options, a society is supposed to have embarked upon a sustainable path. How do we model these variables and the contextual dimensions such that motivation for designing and delivery of innovation is empathetic, reciprocal, responsible and respectful of community creativity, aspirations and even contradictions. Returning from the northern tip of india, near line of control, Gurej valley, Jammu and Kashmir after walking for a week through the mountains with sub-zero temperature in the night, the contradictions in development process are quite evident. One room of a wooden house needs about 50-70 kg of wood daily to keep it warm. With about three months of complete cut off due to 20 feet or more of snow fall, the regions needs a lot of wood. The combustion efficiency of bukhari- the warming device is quite low. A grassroots innovator Tawseef from j&k scouted by the Honey Bee Network volunteers and supported by National Innovation Foundation has achieved a breakthrough design that can warm the house for eight hours with just three to Four kg of wood. Women who harvest and bring the heavy loads of woods on their ill designed baskets from high slopes might get a little reprieve if the new Bukhari is diffused. How do we value the conservation of forest, soil, reduction in landslide and glacial flow, to price the new Bukhari appropriately though ecological-economic modelling? Policy makers may dislike the term subsidy but will they ignore the cost of environmental loss, high drudgery, enormous back pain, gender bias Etc.? It is important for statisticians to properly model the situations like these to ensure that short-term calculations donâ€™t make transition to sustainable future difficult if not impossible. COLLOQUIUMTitle :Multiplicity theorem of singular Spectrum for general Anderson type HamiltonianSpeaker : 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. COLLOQUIUMTitle :A complete class of Type 1 optimal block designs with unequal replicationsSpeaker : 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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