BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Cristian Micheletti (International School for Advanced Studies) DTSTART:20210614T150000Z DTEND:20210614T153000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/1 DESCRIPTION:Title: Knots and links in channel and slit confinement: static and dynamics< /a>\nby Cristian Micheletti (International School for Advanced Studies) as part of BIRS workshop : Novel Mathematical Methods in Material Science: A pplications to Biomaterials\n\n\nAbstract\nI will report on a series of st udies where we looked at how the static and dynamics of entangled polymers is affected by confinement. Specifically\, I will first by consider the k notting of semi-flexible chains inside channels of different size and disc uss how the size and complexity evolves during the free or externally-driv en dynamics of the chain[1\,2]. Next\, I will turn to the case of linked r ings inside channels and slits and discuss how the size and dynamics of th eir linked portion responds to different types of confinement[3\,4].\n\nRe ferences\n[1] C. Micheletti and E. Orlandini\, ”Knotting and unknotting dynamics of DNA strands in nanochannels”\, ACS Macro Letters\, 3 \, 876- 880 (2014)\n[2] D. Michieletto\, E. Orlandini\, M.S. Turner and C. Michele tti\, ”Separation of Geometrical and Topological entangle- ment in Confi ned polymers Driven out of Equilibrium”\, ACS Macro Letters\, 9 \, 1081- 1085 (2020)\n[3] G. D’Adamo\, E. Orlandini and C. Micheletti\, ”Linkin g of ring polymers in slit-like confinement”\, Macromolecules\,\, 50 \, 1713-1718 (2017)\n[4] G. Amici\, M. Caraglio\, E. Orlandini and C. Michele tti\, ”Topologically Linked Chains in Confinement”\, ACS Macro Lett.\, 8 \, 442-446 (2019)\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Fred MacKintosh (Rice University) DTSTART:20210614T153000Z DTEND:20210614T160000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/2 DESCRIPTION:Title: Mechanical phase transitions and elastic anomalies in biopolymer gels \nby Fred MacKintosh (Rice University) as part of BIRS workshop : Nove l Mathematical Methods in Material Science: Applications to Biomaterials\n \n\nAbstract\nThe mechanics of cells and tissues are largely governed by s caffolds of filamentous proteins that make up the cytoskeleton\, as well a s extracellular matrices. Evidence is emerging that such networks can exhi bit rich mechanical phase behavior. A classic example of a mechanical phas e transition was identified by Maxwell for macroscopic engineering structu res: networks of struts or springs exhibit a continuous\, second-order pha se transition at the isostatic point\, where the number of constraints imp osed by connectivity just equals the number of mechanical degrees of freed om. We will present recent theoretical predictions and experimental eviden ce for a strain-controlled mechanical phase transition in biopolymer netwo rks below Maxwell’s isostatic point. We will outline a theoretical frame work to understand and quantify the critical phenomena associated with thi s transition. As we show\, this transition also governs elastic anomalies\ , including an anomalously large Poisson ratio and inverse Poynting effect .\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Wilma Olson (Rutgers University) DTSTART:20210614T160000Z DTEND:20210614T163000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/3 DESCRIPTION:Title: Surprising Twists in Nucleosomal DNA with Implication for Higher-orde r Chromatin Folding\nby Wilma Olson (Rutgers University) as part of BI RS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nWhile nucleosomes are dynamic entities tha t must undergo structural deformations to perform their functions\, the ge neral view from available high-resolution structures is a largely static o ne. Even though numerous examples of twist defects have been documented\, the DNA wrapped around the histone core is generally thought to be overtwi sted. Analysis of available high-resolution structures reveals a heterogen eous distribution of twist along the nucleosomal DNA\, with clear patterns that are consistent with the literature\, and a significant fraction of s tructures that are undertwisted. The subtle differences in nucleosomal DNA folding\, which extend beyond twist\, have implications for nucleosome di sassembly and modeled higher-order structures. Simulations of oligonucleos ome arrays built with undertwisted models behave very differently from tho se constructed from overtwisted models\, in terms of compaction and inter- nucleosome contacts\, introducing configurational changes equivalent to th ose associated with 2-3 base-pair changes in nucleosome spacing. Differenc es in the nucleosomal DNA pathway\, which underlie the way that DNA enters and exits the nucleosome\, give rise to different nucleosome-decorated mi nicircles and affect the topological mix of configurational states.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Kauffman (University of Illinois at Chicago) DTSTART:20210614T164500Z DTEND:20210614T171500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/4 DESCRIPTION:Title: Knotoids and Their Applications\nby Louis Kauffman (University of Illinois at Chicago) as part of BIRS workshop : Novel Mathematical Method s in Material Science: Applications to Biomaterials\n\n\nAbstract\nA knoto id is a generalization of a 1-1 tangle in classical knot theory to a diagr am with ends so that the ends can be in distinct regions.\nSuch diagrams a re taken up to Reidemeister moves that do not allow passage of strands acr oss the ends of the diagram. In this way one obtains\na concept of an open ended diagram that can be classified topologically just as are the closed diagrams of classical knot theory. By constructions due to Vladimir Turae v\n(for diagrams on the two-sphere) and the author and Neslihan Gugumcu (f or diagrams in the plane) one can interpret knotoids as projections from o pen-ended curves in three dimsensional space.\nBy natural restrictions of the isotopies of such space curves (in relation to the projection) one the n has a way to handle the topology of open-ended curves in three dimension al space. This talk will discuss\nthe relationship between open-ended curv es in three dimensional space and their corresponding knotoid classes. We will discuss basic invariants such as the Jones polynomial\, relationships of knotoids with viritual\nknot theory and aspects of our joint work with Nesilhan Gugumcu\, Sofia Lambropoulou\,Manos Manouras and with Eleni Pan agiotou.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleni Panagiotou (University of Tennessee at Chattanooga) DTSTART:20210614T171500Z DTEND:20210614T174500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/5 DESCRIPTION:Title: Effects of topological entanglement on mechanical properties of mater ial\nby Eleni Panagiotou (University of Tennessee at Chattanooga) as p art of BIRS workshop : Novel Mathematical Methods in Material Science: App lications to Biomaterials\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Slobodan Zumer (Jozef Stefan Institute & University of Ljubljana) DTSTART:20210615T140000Z DTEND:20210615T143000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/6 DESCRIPTION:Title: Topological analysis of 3D active nematic turbulence in droplets\ nby Slobodan Zumer (Jozef Stefan Institute & University of Ljubljana) as p art of BIRS workshop : Novel Mathematical Methods in Material Science: App lications to Biomaterials\n\n\nAbstract\nIn confined active anisotropic so ft mater\, the interplay of ordering\, elasticity\, chirality\, confinemen t\, surface anchoring\, external fields\, flows\, and activity leads to nu merous complex static and dynamic structures. Their orientational ordering fields include singular topological defects and nonsingular solitonic def ormations. Increasing interest in active systems stimulated us to model to pology of three-dimensional extensile activity driven nematodynamics in a spherical confinement providing a topological constrain [1\,2]. We used a simple mesoscopic modelling of active nematic fluids [3] that enables nume rical simulations of active nematodynamics. It reasonably well describes e xperiments in thin layers and shells with active complex fluids that are m ostly biological systems driven by internal conversion of stored chemical energy into motion [3\,4]. We demonstrated that at low activity stationary dynamic structures occur that with increasing activity undergo transition s from stationary to chaotic 3D motions - active nematic turbulence. In th is talk I will present how in a such regime the time evolution can be for a specific confinement characterized by a series of elementary topological events where nematic disclinations divide\, merge\, annihilate\, and cros sover. I will focus to homeotropic anchoring\, no-slip surface\, and for s elected activities illustrate our findings by simulated dynamics of nemati c disclinations & flows accompanied by simulated optical microscopy. Our s imple confined system could be a nice test ground for recently introduced machine learning approach to active nematics [5]. \nThe research was done in collaboration with S. Čopar\, J. Aplinc\, Ž. Kos\, and M. Ravnik.\n\n [1] S. Čopar\, J. Aplinc\, Ž. Kos\, S. Žumer\, and M. Ravnik\, Topology of three-dimensional active nematic turbulence confined to droplets\, Phy sical Review X 9\, 031051 (2019)\,\n[2] J. Binysh\, Z. Kos\, S. Čopar\, M . Ravnik\, and G. P. Alexander\, Three-dimensional active defect loops\, P hysical Review Letters 124\, 088001 (2020). \n[3] A. Doostmohammadi\, J. I gnés-Mullol\, and J. M. Yeomans\, F. Sagúes\, Active nematics\, Nature C ommunications 9: 3246\, 1 (2018).\n[4] G. Duclos\, R. Adkins\, D. Banerjee \, M. S. Peterson\, M. Varghese\, I. Kolvin\, A. Baskaran\, R. A. Pelcovit s\, T. R. Powers\, A. Baskaran\, F. Toschi\, M. F. Hagan\, S.J. Streichan\ , V. Vitelli\, D. A. Beller\, and Z. Dogic\, Topological structure and dy namics of three dimensional active nematics\, Science 367\, 1120 (2020).\n [5] J. Colen\, M.Han\, R. Zhang\, S. A. Redford\, L. M. Lemma\, L. Morgan\ , P. V Ruijgrok\, R.Adkins\, Z. Bryant\, Z. Dogic\, M. L. Gardel\, J. J de Pablo\, V. Vitelli\, Machine learning active-nematic hydrodynamics\, Proc . Natl. Acad. Sci. USA 118\, e2016708118 (2021).\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Rajeev Kumar (Oak Ridge National Laboratories) DTSTART:20210615T143000Z DTEND:20210615T150000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/7 DESCRIPTION:Title: Generating Knotted Configurations in Polymers using Field Theory Appr oach\nby Rajeev Kumar (Oak Ridge National Laboratories) as part of BIR S workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nIn this talk\, I will present our on-going work related to understanding topological effects in polymer melts and sol utions. In particular\, issue of Gauge invariance in the field theory of p olymers will be discussed and it will be shown that Gauge fixing can be us ed to discover topological invariants. A specific example using the Coulom b gauge will be used to demonstrate that the helicity is one of the topolo gical invariants for both\, linear and ring polymers. Furthermore\, a nume rical recipe to generate knotted vector fields will be presented for study ing topological configurations near equilibrium using the self-consistent field theory of polymers.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Zidovska (New York University) DTSTART:20210615T150000Z DTEND:20210615T153000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/8 DESCRIPTION:Title: Interphase Chromatin Undergoes a Local Sol-Gel Transition Upon Cell D ifferentiation\nby Alexandra Zidovska (New York University) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applicati ons to Biomaterials\n\n\nAbstract\nCell differentiation\, the process by w hich stem cells become specialized cells\, is associated with chromatin re organization inside the cell nucleus. Here\, we measure the chromatin dist ribution and dynamics in embryonic stem cells in vivo before and after dif ferentiation. We find that undifferentiated chromatin is less compact\, mo re homogeneous and more dynamic than differentiated chromatin. Further\, w e present a noninvasive rheological analysis using intrinsic chromatin dyn amics\, which reveals that undifferentiated chromatin behaves like a Maxwe ll fluid\, while differentiated chromatin shows a coexistence of fluid-lik e (sol) and solid-like (gel) phases. Our data suggest that chromatin under goes a local sol-gel transition upon cell differentiation\, corresponding to the formation of the more dense and transcriptionally inactive heteroch romatin (Eshghi I\, Eaton JA and Zidovska A\, Phys. Rev. Lett.\, 2021).\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/8/ END:VEVENT BEGIN:VEVENT SUMMARY:David Swigon (University of Pittsburgh) DTSTART:20210615T154500Z DTEND:20210615T161500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/9 DESCRIPTION:Title: Dynamical and stochastic simulations of knotted and linked DNA\nb y David Swigon (University of Pittsburgh) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\ n\nAbstract\nPresented will be two methods that allow the study of the sto chastic and dynamical behavior of knotted and confined DNA molecules. One method is based on exact statistical sampling of closed configurations\, t he other on dynamical simulations performed using on generalized immersed boundary method. The equations of motion of the rod include the fluid–st ructure interaction\, sequence-dependent elasticity and a combination of t wo interactions that prevent self-contact\, namely the electrostatic inter action and hard-core repulsion. I will discuss the dynamics of DNA trefoil s and configurations of DNA Hopf links with relevance to kinetoplast DNA.\ n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Javier Arsuaga (University of California\, Davis) DTSTART:20210615T161500Z DTEND:20210615T164500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/10 DESCRIPTION:Title: DNA knots and liquid crystals in icosahedral bacteriophages\nby Javier Arsuaga (University of California\, Davis) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomate rials\n\n\nAbstract\nThe three dimensional organization of genomes is a ke y player in multiple biological processes including the genome packaging a nd release in viruses. The genome of some viruses\, such as bacteriophages or human herpes\, is a double stranded DNA (dsDNA) molecule that is store d inside a viral protein capsid at a concentration of 200 mg/ml-800mg/ml a nd an osmotic pressure of 70 atmospheres. The organization of the viral ge nome under these extreme physical conditions is believed to be liquid crys talline but remains to be properly understood. A general picture of this o rganization has been recently given by cryoelectron microscopy (cryoEM) st udies that show a series of concentric layers near the surface of the vira l capsid followed by a disordered arrangement of DNA fibers near the cente r of the capsid.\nIn this talk I will present computational and experiment al results modeling the structure and packing of DNA in bacteriophage P4. P4 is characterized for producing DNA knots and for being one of the small est bacteriophages with only 45nm in diameter. I will discuss experimental results concerning the structure of P4 and how liquid crystal models can help predict the properties of DNA in P4 and the formation of knots.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Tetsuo Deguchi (Ochanomizu University) DTSTART:20210616T140000Z DTEND:20210616T143000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/11 DESCRIPTION:Title: Exact evaluation of the mean-square fluctuation of the position vect or of a crosslinking point in the Gaussian network\nby Tetsuo Deguchi (Ochanomizu University) as part of BIRS workshop : Novel Mathematical Meth ods in Material Science: Applications to Biomaterials\n\n\nAbstract\nThe G aussian network plays a central role in the study on the fundamental elast ic behavior\nof various polymer networks such as rubbers and gels [1\, 2]. Here we remark that many\nbio-materials are made of gels. Recently\, a ne w method has been introduced for generating\nan ensemble of random conform ations of graph-shaped polymers in terms of topologically constrained\nGau ssian random walks (TCRW) or Gaussian random graph embeddings [3]. It is o ne\nof the key properties of TCRW that the probability distribution functi on of the bond vectors in\npolymer conformations of TCRW is composed of th e normal distributions with unit variance.\nIn this talk we critically stu dy Flory’s approximate expression for the mean square fluctuation\nof th e end-to-end vector r around its average value \\(r\\) with functionality \\(f\\) [4]\n\n$$⟨2 ⟨(r − ⟨r⟩) ⟩2 2Nb f$$\n\nHere N is the number of the Kuhn segments in the network subchain connecting a crosslin king\npoint to another one.\nWe express the fluctuation ⟨(Δr)2⟩ in te rms of resistance distances\, and evaluate it rigorously.\nWe argue that F lory’ s expression should be valid if the functionality f is very large\ ,\nbased on the numerical experiments of large random graphs with function ality f\, i.e.\, regular\ngraphs with functionality f. We also discuss the results of Ref. [5].\nThe results of the present talk should be important not only in materials science but also\nin applications of biomaterials.\ n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefanie Redemann (University of Virginia) DTSTART:20210616T143000Z DTEND:20210616T150000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/12 DESCRIPTION:Title: Integrated 3D tomography and computational modeling to study mechani cs in mitotic and meiotic spindles\nby Stefanie Redemann (University o f Virginia) as part of BIRS workshop : Novel Mathematical Methods in Mater ial Science: Applications to Biomaterials\n\n\nAbstract\nThe faithful segr egation of chromosomes during mitosis is a fundamental and important proce ss. Errors in mitosis have severe implications and are often detrimental to development\, health and survival of the organism. We know that microtu bules\, in particular kinetochore microtubules\, exert forces on chromosom es to initially position them on the metaphase plate and consequently divi de them to the two daughter cells. The forces generated by microtubules ar e in balance during metaphase resulting in a mechanical steady-state and a stable long-lived spindle shape and length. Previous studies have identif ied the proteins involved in metaphase spindle assembly. Yet\, we do not u nderstand how those proteins lead to force generation through interactions of microtubules\, motor proteins and chromosomes in submicron scale\, and the collective effect of these forces on spindle shape function at larger scales. One major barrier in answering this question is the limitation of light microscopy in visualizing details of spindle microstructure in subm icron resolutions. We have developed a novel approach of visualizing entir e spindles in 3D by electron tomography and automatic microtubule segmenta tion. Using this approach\, we can resolve single microtubules\, which pro vides a unique perspective and offers a plethora of completely new informa tion about the microstructure of spindles. Specifically\, we can resolve c hromosome surfaces\, identify microtubules that are in contact with chromo somes (kinetochore microtubules)\, determine microtubules’ nucleation pr ofile\, length distribution and local curvature. We combine electron tomog raphy\, light microcopy\, biophysical modeling and large-scale simulations to develop a detailed and unprecedented understanding of force generation inside the spindle from individual microtubules to the mitotic spindle co mposed of thousands of microtubules.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg Lavrentovich (University of Virginia) DTSTART:20210616T150000Z DTEND:20210616T153000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/13 DESCRIPTION:Title: Tactoid-to-Toroid Topological Transition (4T-transition ot T5) in Li quid Crystal Nuclei\nby Oleg Lavrentovich (University of Virginia) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Ap plications to Biomaterials\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine Soteros (University of Saskatchewan) DTSTART:20210616T154500Z DTEND:20210616T161500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/14 DESCRIPTION:Title: Characterizing linking in lattice models of polymers in nanochannels \nby Christine Soteros (University of Saskatchewan) as part of BIRS wo rkshop : Novel Mathematical Methods in Material Science: Applications to B iomaterials\n\n\nAbstract\nMotivated in part by experimental and molecula r dynamics studies of the entanglement characteristics of DNA in nanonchan nels\, we have been studying the statistics of knotting and linking for eq uilibrium lattice models of polymers confined to lattice tubes. In this t alk I will present our theorems and transfer-matrix-based numerical result s for the link statistics for self-avoiding polygon models in small tubes. The main focus will be on the special case of pairs of polygons which s pan a lattice tube. In this case\, it is known that all but exponentially few of the configurations will be linked as the span of the polygons goes to infinity. However there are many interesting open questions about conf igurational statistics for pairs of polygons with fixed link type and I wi ll introduce some of those.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Franziska Weber (Carnegie Mellon University) DTSTART:20210616T161500Z DTEND:20210616T164500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/15 DESCRIPTION:Title: A Convergent Numerical Method for a Model of Liquid Crystal Director Coupled to An Electric Field\nby Franziska Weber (Carnegie Mellon Uni versity) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nStarting from the Os een-Frank theory\, we derive a simple model for the dynamics of a nematic liquid crystal director field under the influence of an electric field. Th e resulting nonlinear system of partial differential equations consists of the electrostatics equations for the electric field coupled with the damp ed wave map equation for the evolution of the liquid crystal director fiel d\, which is a normal vector pointing in the direction of the main orienta tion of the liquid crystal molecules. The liquid crystal director field en ters the electrostatics equations in the constitutiverelations while the e lectric field enters the wave map equation in the form of a nonlinear sour ce term. Since it is a normal vector\, the variable for the liquid crystal director field has to satisfy the constraint that it takes values in the unit sphere. We derive an energy-stable and constraint preserving numerica l method for this system and prove convergence of a subsequence of approxi mations to a weak solution of the system of partial differential equations . In particular\, this implies the existence of weak solutions for this mo del.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Koya Shimokawa (Saitama University) DTSTART:20210617T140000Z DTEND:20210617T143000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/16 DESCRIPTION:Title: Handlebody decompositions of the 3-torus and polycontinuous patterns \nby Koya Shimokawa (Saitama University) as part of BIRS workshop : No vel Mathematical Methods in Material Science: Applications to Biomaterials \n\n\nAbstract\nPolycontinuous patterns appear as microphase separation of block\ncopolymers. In this talk\, we discuss handlebody decompositions of the\n3-torus and their application to the study of polycontinuous pattern s.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Myfanwy Evans (University of Potsdam) DTSTART:20210617T143000Z DTEND:20210617T150000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/17 DESCRIPTION:Title: Triply-periodic tangling\nby Myfanwy Evans (University of Potsda m) as part of BIRS workshop : Novel Mathematical Methods in Material Scien ce: Applications to Biomaterials\n\n\nAbstract\nUsing periodic surfaces as a scaffold is a convenient route to making periodic entanglements. I will present a systematic way of building new tangled periodic structures\, u sing low-dimensional topology and combinatorics\, posing the question of h ow to characterise the structures more completely.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisabetta Matsumoto (Georgia Tech) DTSTART:20210617T150000Z DTEND:20210617T153000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/18 DESCRIPTION:by Elisabetta Matsumoto (Georgia Tech) as part of BIRS worksho p : Novel Mathematical Methods in Material Science: Applications to Biomat erials\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Radmila Sazdanovic (NC State University) DTSTART:20210617T154500Z DTEND:20210617T161500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/19 DESCRIPTION:Title: TDA applications in cancer genomics\nby Radmila Sazdanovic (NC S tate University) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nCancer is a polygenic disease in which genomic events are selected in order to produce a sophisticated and coordinated outcome. Determining when two events are co-occurring is at the heart of finding possible genetic treatments and al so an important open question in data science. This work focuses on furthe r analysis and modification of the existing topological data analysis appr oach to breast cancer data. In particular we will address the stability of proposed methods and possible generalizations to other contexts.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Harris (NC State University) DTSTART:20210617T161500Z DTEND:20210617T164500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/20 DESCRIPTION:Title: Multiscale Simulations of Biological Polymers\nby Sarah Harris ( NC State University) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nPolymeri c structures are ubiquitous in biology\, and perform diverse functions at multiple length-scales. DNA carries the genetic code through the chemistr y of the constituent bases at an atomic level\, but also plays an active r ole in its own regulation through its ability to store and transmit mechan ical stress over genomic length-scales. Long polymeric coiled-coils are a common protein structural motif\, and as well as forming the basis of rob ust super-macromolecular hierarchical structures such as collagen\, also h ave an active role in regulating the chemo-mechanical cycle of molecular m otors such as dynein and myosin. Intrinsically disordered proteins present a particular enigma\; some undergo disorder to order transitions on encou ntering their binding partner and so participate in highly specific molecu lar recognition in spite of their apparent lack of structure\, whereas oth ers appear to generate vital emergent behaviour over far longer length-sca les than their own structure\, such as the self-assembly of membraneless o rganelles.\nHere I will compare and contrast multi-scale representations o f polymeric biomacromolecules from the fully atomistic up to the continuum level. I will discuss open challenges to development and biological quest ions that would benefit from robust mathematical and computational models of biological polymers.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Rawdon (University of Saint Thomas) DTSTART:20210618T143000Z DTEND:20210618T150000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/21 DESCRIPTION:Title: Accumulated knot probability\nby Eric Rawdon (University of Sain t Thomas) as part of BIRS workshop : Novel Mathematical Methods in Materia l Science: Applications to Biomaterials\n\n\nAbstract\nMany knots in natur e are open knots\, not the closed knots from knot theory. There are sever al definitions of knotting in open curves\, each of which have their own a dvantages and disadvantages. The speaker's favorite open knot definition involves extending rays to infinity in a common direction from the endpoin ts to create a closed knot for each such direction. In such a case\, the knotting in an open chain is classified as the distribution of knot types seen over the different directions of closure. In most cases\, there is a knot type that appears in over 50% of the closure directions\, in which c ase we might all be able to agree that the open knot has the essence of th at closed knot type. However\, there are many cases where there is no kno t type that appears in over 50% of the closure directions\, especially nea r transitions between different knot types. We present the accumulated kn ot probability as a way of making sense of these more ambiguous situations . The short story is that\, for a given knot type K\, we compute the prob ability that the closures are a knot type which "includes" K in some sense . In this talk\, we use the partial ordering on knots developed by Diao\, Ernst\, and Stasiak based on crossing changes in minimal knot diagrams\, which creates a sort of family tree of knots. However\, any sort of famil y tree could be substituted here depending on what one is trying to model. We show how some of the knotting classifications change for some protein s and tight knot configurations.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Pei Liu (University of Minnesota) DTSTART:20210618T150000Z DTEND:20210618T153000Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/22 DESCRIPTION:by Pei Liu (University of Minnesota) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomater ials\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenneth Millett (University of California\, Santa Barbara) DTSTART:20210618T154500Z DTEND:20210618T161500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/23 DESCRIPTION:Title: Using the HOMFLY-PT polynomial to quantuantify the entanglement of c ollections of open chains\nby Kenneth Millett (University of Californi a\, Santa Barbara) as part of BIRS workshop : Novel Mathematical Methods i n Material Science: Applications to Biomaterials\n\n\nAbstract\nThe superp osition of HOMFLY-PT polynomials of collections of open chains provides an "average" of the\npolynomials associated to individual closures and\, con sequently\, a HOMFLY-PT polynomial for the open\nlink. Following a bri\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Rechnitzer (University of California\, Santa Barbara) DTSTART:20210618T161500Z DTEND:20210618T164500Z DTSTAMP:20260422T185046Z UID:BIRS_21w5232/24 DESCRIPTION:Title: Trials and tribulations of preserving topology\nby Andrew Rechni tzer (University of California\, Santa Barbara) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomateri als\n\n\nAbstract\nMonte Carlo simulations are a big part of understanding the statistical properties of knots. Unfortunately\, if one wishes to stu dy curves of fixed knot types then there are very few methods available. T his work\, with Nick Beaton and Nathan Clisby\, is an attempt to adapt exi sting algorithms to polygons in R3 of fixed topology. It is very much a wo rk in progress\, but I will report on our work adapting BFACF to polygons in R3\, and also our attempts at trying to coerce the (very fast) pivot al gorithm to respect topology.\n LOCATION:https://researchseminars.org/talk/BIRS_21w5232/24/ END:VEVENT END:VCALENDAR