#TIBR (The Irregular But Rendered, November 24, 2018):
Can we avoid fractals if we want to? Are our fingers irregular? Is there thumb cancer? Or, toe cancer? Are all regular objects ‘algebraically’ representable? Are cones manifolds? Do cubes have an algebraic description? Can algebraic equations catch everything (?) that topology cannot? Might two visually indistinguishable manifolds vary dramatically? Can circles have a ‘complex’ structure? Do biological objects (including virus) have edges or points? Do multi scale interactions make hearts or kidneys regular? Do biological objects always (always) live in time? Can the open Euclidean space be put ‘inside’ another space? Can shape, volume, and size (say) tell us whether a biological organ is regular? Might there even be regularity across species? When/is cancer growth predictable? Can fractals only be approximated (algebraically)? Why can’t biological objects be thought of only computationally? Is it easy to tell irregularity and complexity apart? Is ‘too complex’ as good as irregular? Can irregularity be no-where-dense? Why is 3-dimensional space much more complicated than spaces with both higher and lower dimensions? Will biology have to take the material properties (hardness, etc.) into account in the future? SynTalk thinks about these & more questions using concepts from cell biology (Dr. Ramray Bhat, IISc, Bangalore), & algebraic geometry (Dr. Amalendu Krishna, TIFR, Mumbai).
SynTalk is pleased and privileged to have hosted the following SynTalkrs (in alphabetical order) on its #TIBR show.
Dr. Ramray Bhat (cell biology) is is an assistant professor in the Biological Sciences Division in the Indian Institute of Science (IISc), Bangalore. He works on questions of pattern formation and deformation in the context of animal development and disease such as cancer. His work has helped showcase the role glycobiology plays both in the establishment and degradation of biological form. Dr. Bhat started off by earning his undergraduate degree in medicine at the University of Calcutta Medical College (Kolkata). He then worked on questions of animal limb development and evolution for his Ph.D. in the New York Medical College (USA). As a Susan G Komen Fellow at Berkeley Labs, California (USA), he worked on problems of breast morphogenesis and cancer. As part of his current research, he & his team are working towards understanding the behavior of cancer cells as they migrate from their primary environment into either solid stromal microenvironments en route vascular channels (such as in breast cancer) or into fluid microenvironments, where the cancer cells face harsh pro-inflammatory anchorage-independent pressures. They are also interested in using the theories and principles of pattern formation and morphogenesis towards devising models for the behavior and assembly of normal and cancer cell collectives. He also serves on the editorial board of ‘Dialogue: Science, Scientists and Society’, a journal by the Indian Academy of Sciences, devoted to examining and renewing the compact between the scientific community and the social milieu its embedded within. When not thinking about science, he loves to read about, and occasionally write on, the interface of politics and culture. Dr. Bhat has been awarded multiple fellowships, including, Intermediate Fellowship, Wellcome Trust DBT India Alliance (2018- present), and the DST SERB Early Career Research Fellow (2016-present).
Dr. Amalendu Krishna (algebraic geometry) is an Associate Professor at the School of Mathematics, Tata Institute of Fundamental Research (TIFR), Mumbai. Prior to this he also served as the Hedrick Assistant Professor, Department of Mathematics, University of California at Los Angeles (UCLA, USA) and also as a Member at the School of Mathematics, Institute for Advanced Study (IAS, Princeton, USA). He completed his Masters in Statistics from Indian Statistical Institute (ISI Kolkata,1996) and then completed his Ph.D. from TIFR (2001). His research interests are algebraic geometry, algebraic K-theory and algebraic cycles. In his work, Dr. Krishna has applied the modern theories of algebraic K-theory and Voevodsky’s theory of motives to study concrete problems. His results on 0-cycles on algebraic varieties with isolated singularities effectively reduces their study to the corresponding study on the desingularization, together with information about multiples of the exceptional divisors. This allows the complete calculation of the Chow group of 0-cycles on an algebraic variety in many cases, like the case of rational varieties or cones. Working initially with Levine, and later with Park, Dr. Krishna has worked to built up the original constructions of Bloch-Esnault on additive Chow groups into a full theory. This includes proving fundamental properties, such as the contravariant functoriality and a projective bundle formula, as well as constructing an action of the usual higher Chow groups on the additive ones. Dr. Krishna is also the editor of the Journal of Ramanujan Mathematical Society (JRMS, since 2016). He has received multiple awards & fellowships, including, B. M. Birla Science Prize in Mathematics (2009), Swarnajayanti Prize in Mathematical Sciences (2011), the ICTP Ramanujan Prize (ICTP, Trieste, 2015), the Shanti Swarup Bhatnagar Prize (Mathematical Sciences, 2016), and the Fellowship of Indian Academy of Sciences (IAS, 2016).
Note: Any & all errors in the brief profiles above are SynTalk’s own.
#TIBR mentions: Henri Poincaré, Karl Weierstrass, Alan Turing, Ray Solomonoff, Gregory Chaitin, Andrey Kolmogorov, John von Neumann, Stanislaw Ulam, Wei-Liang Chow, William Thurston, & Stephen Wolfram, among others.