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:20260404T041200Z UID:BIRS_21w5232/1 DESCRIPTION:Title: Knots and links in channel and slit confinement: static and dy namics\nby Cristian Micheletti (International School for Advanced Stud ies) as part of BIRS workshop : Novel Mathematical Methods in Material Sci ence: Applications to Biomaterials\n\n\nAbstract\nI will report on a serie s of studies where we looked at how the static and dynamics of entangled p olymers is affected by confinement. Specifically\, I will first by conside r the knotting of semi-flexible chains inside channels of different size a nd discuss how the size and complexity evolves during the free or external ly-driven dynamics of the chain[1\,2]. Next\, I will turn to the case of l inked rings inside channels and slits and discuss how the size and dynamic s of their linked portion responds to different types of confinement[3\,4] .\n\nReferences\n[1] C. Micheletti and E. Orlandini\, ”Knotting and unkn otting dynamics of DNA strands in nanochannels”\, ACS Macro Letters\, 3 \, 876-880 (2014)\n[2] D. Michieletto\, E. Orlandini\, M.S. Turner and C. Micheletti\, ”Separation of Geometrical and Topological entangle- ment i n Confined polymers Driven out of Equilibrium”\, ACS Macro Letters\, 9 \ , 1081-1085 (2020)\n[3] G. D’Adamo\, E. Orlandini and C. Micheletti\, ”Linking of ring polymers in slit-like confinement”\, Macromolecules\, \, 50 \, 1713-1718 (2017)\n[4] G. Amici\, M. Caraglio\, E. Orlandini and C . Micheletti\, ”Topologically Linked Chains in Confinement”\, ACS Macr o Lett.\, 8 \, 442-446 (2019)\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Fred MacKintosh (Rice University) DTSTART:20210614T153000Z DTEND:20210614T160000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/2 DESCRIPTION:Title: Mechanical phase transitions and elastic anomalies in biopolym er gels\nby Fred MacKintosh (Rice University) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomate rials\n\n\nAbstract\nThe mechanics of cells and tissues are largely govern ed by scaffolds of filamentous proteins that make up the cytoskeleton\, as well as extracellular matrices. Evidence is emerging that such networks c an exhibit rich mechanical phase behavior. A classic example of a mechanic al phase transition was identified by Maxwell for macroscopic engineering structures: networks of struts or springs exhibit a continuous\, second-or der phase transition at the isostatic point\, where the number of constrai nts imposed by connectivity just equals the number of mechanical degrees o f freedom. We will present recent theoretical predictions and experimental evidence for a strain-controlled mechanical phase transition in biopolyme r networks below Maxwell’s isostatic point. We will outline a theoretica l framework to understand and quantify the critical phenomena associated w ith this transition. As we show\, this transition also governs elastic ano malies\, including an anomalously large Poisson ratio and inverse Poynting effect.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Wilma Olson (Rutgers University) DTSTART:20210614T160000Z DTEND:20210614T163000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/3 DESCRIPTION:Title: Surprising Twists in Nucleosomal DNA with Implication for High er-order Chromatin Folding\nby Wilma Olson (Rutgers University) as par t of BIRS workshop : Novel Mathematical Methods in Material Science: Appli cations to Biomaterials\n\n\nAbstract\nWhile nucleosomes are dynamic entit ies that must undergo structural deformations to perform their functions\, the general view from available high-resolution structures is a largely s tatic one. Even though numerous examples of twist defects have been docume nted\, the DNA wrapped around the histone core is generally thought to be overtwisted. Analysis of available high-resolution structures reveals a he terogeneous distribution of twist along the nucleosomal DNA\, with clear p atterns that are consistent with the literature\, and a significant fracti on of structures that are undertwisted. The subtle differences in nucleoso mal DNA folding\, which extend beyond twist\, have implications for nucleo some disassembly and modeled higher-order structures. Simulations of oligo nucleosome arrays built with undertwisted models behave very differently f rom those constructed from overtwisted models\, in terms of compaction and inter-nucleosome contacts\, introducing configurational changes equivalen t to those associated with 2-3 base-pair changes in nucleosome spacing. Di fferences in the nucleosomal DNA pathway\, which underlie the way that DNA enters and exits the nucleosome\, give rise to different nucleosome-decor ated minicircles and affect the topological mix of configurational states. \n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis Kauffman (University of Illinois at Chicago) DTSTART:20210614T164500Z DTEND:20210614T171500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/4 DESCRIPTION:Title: Knotoids and Their Applications\nby Louis Kauffman (Univer sity of Illinois at Chicago) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\n A knotoid is a generalization of a 1-1 tangle in classical knot theory to a diagram with ends so that the ends can be in distinct regions.\nSuch dia grams are taken up to Reidemeister moves that do not allow passage of stra nds across 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 Vladimi r Turaev\n(for diagrams on the two-sphere) and the author and Neslihan Gug umcu (for diagrams in the plane) one can interpret knotoids as projections from open-ended curves in three dimsensional space.\nBy natural restricti ons of the isotopies of such space curves (in relation to the projection) one then has a way to handle the topology of open-ended curves in three di mensional space. This talk will discuss\nthe relationship between open-end ed curves in three dimensional space and their corresponding knotoid class es. We will discuss basic invariants such as the Jones polynomial\, relati onships of knotoids with viritual\nknot theory and aspects of our joint wo rk with Nesilhan Gugumcu\, Sofia Lambropoulou\,Manos Manouras and with El eni Panagiotou.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Eleni Panagiotou (University of Tennessee at Chattanooga) DTSTART:20210614T171500Z DTEND:20210614T174500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/5 DESCRIPTION:Title: Effects of topological entanglement on mechanical properties o f material\nby Eleni Panagiotou (University of Tennessee at Chattanoog a) as part of BIRS workshop : Novel Mathematical Methods in Material Scien ce: Applications to Biomaterials\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Slobodan Zumer (Jozef Stefan Institute & University of Ljubljana) DTSTART:20210615T140000Z DTEND:20210615T143000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/6 DESCRIPTION:Title: Topological analysis of 3D active nematic turbulence in drople ts\nby Slobodan Zumer (Jozef Stefan Institute & University of Ljubljan a) as part of BIRS workshop : Novel Mathematical Methods in Material Scien ce: Applications to Biomaterials\n\n\nAbstract\nIn confined active anisotr opic soft mater\, the interplay of ordering\, elasticity\, chirality\, con finement\, surface anchoring\, external fields\, flows\, and activity lead s to numerous complex static and dynamic structures. Their orientational o rdering fields include singular topological defects and nonsingular solito nic deformations. Increasing interest in active systems stimulated us to m odel topology of three-dimensional extensile activity driven nematodynamic s in a spherical confinement providing a topological constrain [1\,2]. We used a simple mesoscopic modelling of active nematic fluids [3] that enabl es numerical simulations of active nematodynamics. It reasonably well desc ribes experiments in thin layers and shells with active complex fluids tha t are mostly biological systems driven by internal conversion of stored ch emical energy into motion [3\,4]. We demonstrated that at low activity sta tionary dynamic structures occur that with increasing activity undergo tra nsitions from stationary to chaotic 3D motions - active nematic turbulence . In this talk I will present how in a such regime the time evolution can be for a specific confinement characterized by a series of elementary topo logical events where nematic disclinations divide\, merge\, annihilate\, a nd crossover. I will focus to homeotropic anchoring\, no-slip surface\, an d for selected activities illustrate our findings by simulated dynamics of nematic disclinations & flows accompanied by simulated optical microscopy . Our simple confined system could be a nice test ground for recently intr oduced machine learning approach to active nematics [5]. \nThe research wa s done in collaboration with S. Čopar\, J. Aplinc\, Ž. Kos\, and M. Ravn ik.\n\n[1] S. Čopar\, J. Aplinc\, Ž. Kos\, S. Žumer\, and M. Ravnik\, T opology of three-dimensional active nematic turbulence confined to droplet s\, Physical Review X 9\, 031051 (2019)\,\n[2] J. Binysh\, Z. Kos\, S. Čo par\, M. Ravnik\, and G. P. Alexander\, Three-dimensional active defect lo ops\, Physical Review Letters 124\, 088001 (2020). \n[3] A. Doostmohammadi \, J. Ignés-Mullol\, and J. M. Yeomans\, F. Sagúes\, Active nematics\, N ature Communications 9: 3246\, 1 (2018).\n[4] G. Duclos\, R. Adkins\, D. B anerjee\, M. S. Peterson\, M. Varghese\, I. Kolvin\, A. Baskaran\, R. A. P elcovits\, T. R. Powers\, A. Baskaran\, F. Toschi\, M. F. Hagan\, S.J. Str eichan\, V. Vitelli\, D. A. Beller\, and Z. Dogic\, Topological structure and dynamics of three dimensional active nematics\, Science 367\, 1120 (2 020).\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://stable.researchseminars.org/talk/BIRS_21w5232/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Rajeev Kumar (Oak Ridge National Laboratories) DTSTART:20210615T143000Z DTEND:20210615T150000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/7 DESCRIPTION:Title: Generating Knotted Configurations in Polymers using Field Theo ry Approach\nby Rajeev Kumar (Oak Ridge National Laboratories) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applic ations to Biomaterials\n\n\nAbstract\nIn this talk\, I will present our on -going work related to understanding topological effects in polymer melts and solutions. In particular\, issue of Gauge invariance in the field theo ry of polymers will be discussed and it will be shown that Gauge fixing ca n be used to discover topological invariants. A specific example using the Coulomb gauge will be used to demonstrate that the helicity is one of the topological invariants for both\, linear and ring polymers. Furthermore\, a numerical recipe to generate knotted vector fields will be presented fo r studying topological configurations near equilibrium using the self-cons istent field theory of polymers.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexandra Zidovska (New York University) DTSTART:20210615T150000Z DTEND:20210615T153000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/8 DESCRIPTION:Title: Interphase Chromatin Undergoes a Local Sol-Gel Transition Upon Cell Differentiation\nby Alexandra Zidovska (New York University) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Ap plications to Biomaterials\n\n\nAbstract\nCell differentiation\, the proce ss by which stem cells become specialized cells\, is associated with chrom atin reorganization inside the cell nucleus. Here\, we measure the chromat in distribution and dynamics in embryonic stem cells in vivo before and af ter differentiation. We find that undifferentiated chromatin is less compa ct\, more homogeneous and more dynamic than differentiated chromatin. Furt her\, we present a noninvasive rheological analysis using intrinsic chroma tin dynamics\, which reveals that undifferentiated chromatin behaves like a Maxwell fluid\, while differentiated chromatin shows a coexistence of fl uid-like (sol) and solid-like (gel) phases. Our data suggest that chromati n undergoes a local sol-gel transition upon cell differentiation\, corresp onding to the formation of the more dense and transcriptionally inactive h eterochromatin (Eshghi I\, Eaton JA and Zidovska A\, Phys. Rev. Lett.\, 20 21).\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/8/ END:VEVENT BEGIN:VEVENT SUMMARY:David Swigon (University of Pittsburgh) DTSTART:20210615T154500Z DTEND:20210615T161500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/9 DESCRIPTION:Title: Dynamical and stochastic simulations of knotted and linked DNA \nby David Swigon (University of Pittsburgh) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomater ials\n\n\nAbstract\nPresented will be two methods that allow the study of the stochastic and dynamical behavior of knotted and confined DNA molecule s. One method is based on exact statistical sampling of closed configurati ons\, the other on dynamical simulations performed using on generalized im mersed boundary method. The equations of motion of the rod include the flu id–structure interaction\, sequence-dependent elasticity and a combinati on of two interactions that prevent self-contact\, namely the electrostati c interaction and hard-core repulsion. I will discuss the dynamics of DNA trefoils and configurations of DNA Hopf links with relevance to kinetoplas t DNA.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Javier Arsuaga (University of California\, Davis) DTSTART:20210615T161500Z DTEND:20210615T164500Z DTSTAMP:20260404T041200Z 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 w orkshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nThe three dimensional organization of genomes is a key player in multiple biological processes including the genome pack aging and release in viruses. The genome of some viruses\, such as bacteri ophages or human herpes\, is a double stranded DNA (dsDNA) molecule that i s stored inside a viral protein capsid at a concentration of 200 mg/ml-800 mg/ml and an osmotic pressure of 70 atmospheres. The organization of the v iral genome under these extreme physical conditions is believed to be liqu id crystalline but remains to be properly understood. A general picture of this organization has been recently given by cryoelectron microscopy (cry oEM) studies that show a series of concentric layers near the surface of t he viral capsid followed by a disordered arrangement of DNA fibers near th e center of the capsid.\nIn this talk I will present computational and exp erimental results modeling the structure and packing of DNA in bacteriopha ge P4. P4 is characterized for producing DNA knots and for being one of th e smallest bacteriophages with only 45nm in diameter. I will discuss exper imental results concerning the structure of P4 and how liquid crystal mode ls can help predict the properties of DNA in P4 and the formation of knots .\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Tetsuo Deguchi (Ochanomizu University) DTSTART:20210616T140000Z DTEND:20210616T143000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/11 DESCRIPTION:Title: Exact evaluation of the mean-square fluctuation of the positi on vector of a crosslinking point in the Gaussian network\nby Tetsuo D eguchi (Ochanomizu University) as part of BIRS workshop : Novel Mathematic al Methods in Material Science: Applications to Biomaterials\n\n\nAbstract \nThe Gaussian network plays a central role in the study on the fundamenta l elastic 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 new method has been introduced for generating\nan ensemble of random conformations of graph-shaped polymers in terms of topologically constrain ed\nGaussian random walks (TCRW) or Gaussian random graph embeddings [3]. It is one\nof the key properties of TCRW that the probability distribution function of the bond vectors in\npolymer conformations of TCRW is compose d of the normal distributions with unit variance.\nIn this talk we critica lly study Flory’s approximate expression for the mean square fluctuation \nof the end-to-end vector r around its average value \\(r\\) with functio nality \\(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 c rosslinking\npoint to another one.\nWe express the fluctuation ⟨(Δr)2 ⟩ in terms of resistance distances\, and evaluate it rigorously.\nWe arg ue that Flory’ s expression should be valid if the functionality f is ve ry large\,\nbased on the numerical experiments of large random graphs with functionality f\, i.e.\, regular\ngraphs with functionality f. We also di scuss the results of Ref. [5].\nThe results of the present talk should be important not only in materials science but also\nin applications of bioma terials.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefanie Redemann (University of Virginia) DTSTART:20210616T143000Z DTEND:20210616T150000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/12 DESCRIPTION:Title: Integrated 3D tomography and computational modeling to study mechanics in mitotic and meiotic spindles\nby Stefanie Redemann (Unive rsity of Virginia) as part of BIRS workshop : Novel Mathematical Methods i n Material Science: Applications to Biomaterials\n\n\nAbstract\nThe faithf ul segregation of chromosomes during mitosis is a fundamental and importan t process. Errors in mitosis have severe implications and are often detri mental to development\, health and survival of the organism. We know that microtubules\, in particular kinetochore microtubules\, exert forces on ch romosomes to initially position them on the metaphase plate and consequent ly divide them to the two daughter cells. The forces generated by microtub ules are in balance during metaphase resulting in a mechanical steady-stat e and a stable long-lived spindle shape and length. Previous studies have identified the proteins involved in metaphase spindle assembly. Yet\, we d o not understand how those proteins lead to force generation through inter actions of microtubules\, motor proteins and chromosomes in submicron scal e\, and the collective effect of these forces on spindle shape function at larger scales. One major barrier in answering this question is the limita tion of light microscopy in visualizing details of spindle microstructure in submicron resolutions. We have developed a novel approach of visualizin g entire spindles in 3D by electron tomography and automatic microtubule s egmentation. Using this approach\, we can resolve single microtubules\, wh ich provides a unique perspective and offers a plethora of completely new information about the microstructure of spindles. Specifically\, we can re solve chromosome surfaces\, identify microtubules that are in contact with chromosomes (kinetochore microtubules)\, determine microtubules’ nuclea tion profile\, length distribution and local curvature. We combine electro n tomography\, light microcopy\, biophysical modeling and large-scale simu lations to develop a detailed and unprecedented understanding of force gen eration inside the spindle from individual microtubules to the mitotic spi ndle composed of thousands of microtubules.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Oleg Lavrentovich (University of Virginia) DTSTART:20210616T150000Z DTEND:20210616T153000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/13 DESCRIPTION:Title: Tactoid-to-Toroid Topological Transition (4T-transition ot T5 ) in Liquid Crystal Nuclei\nby Oleg Lavrentovich (University of Virgin ia) as part of BIRS workshop : Novel Mathematical Methods in Material Scie nce: Applications to Biomaterials\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Christine Soteros (University of Saskatchewan) DTSTART:20210616T154500Z DTEND:20210616T161500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/14 DESCRIPTION:Title: Characterizing linking in lattice models of polymers in nanoc hannels\nby Christine Soteros (University of Saskatchewan) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applicatio ns to Biomaterials\n\n\nAbstract\nMotivated in part by experimental and m olecular dynamics studies of the entanglement characteristics of DNA in na nonchannels\, we have been studying the statistics of knotting and linking for equilibrium lattice models of polymers confined to lattice tubes. In this talk I will present our theorems and transfer-matrix-based numerical results 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 span a lattice tube. In this case\, it is known that all but exponen tially few of the configurations will be linked as the span of the polygon s goes to infinity. However there are many interesting open questions abo ut configurational statistics for pairs of polygons with fixed link type a nd I will introduce some of those.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Franziska Weber (Carnegie Mellon University) DTSTART:20210616T161500Z DTEND:20210616T164500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/15 DESCRIPTION:Title: A Convergent Numerical Method for a Model of Liquid Crystal D irector Coupled to An Electric Field\nby Franziska Weber (Carnegie Mel lon University) as part of BIRS workshop : Novel Mathematical Methods in M aterial Science: Applications to Biomaterials\n\n\nAbstract\nStarting from the Oseen-Frank theory\, we derive a simple model for the dynamics of a n ematic liquid crystal director field under the influence of an electric fi eld. The resulting nonlinear system of partial differential equations cons ists of the electrostatics equations for the electric field coupled with t he damped wave map equation for the evolution of the liquid crystal direct or field\, which is a normal vector pointing in the direction of the main orientation of the liquid crystal molecules. The liquid crystal director f ield enters the electrostatics equations in the constitutiverelations whil e the electric field enters the wave map equation in the form of a nonline ar source 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 n umerical method for this system and prove convergence of a subsequence of approximations to a weak solution of the system of partial differential eq uations. In particular\, this implies the existence of weak solutions for this model.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Koya Shimokawa (Saitama University) DTSTART:20210617T140000Z DTEND:20210617T143000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/16 DESCRIPTION:Title: Handlebody decompositions of the 3-torus and polycontinuous p atterns\nby Koya Shimokawa (Saitama University) as part of BIRS worksh op : Novel Mathematical Methods in Material Science: Applications to Bioma terials\n\n\nAbstract\nPolycontinuous patterns appear as microphase separa tion of block\ncopolymers. In this talk\, we discuss handlebody decomposit ions of the\n3-torus and their application to the study of polycontinuous patterns.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Myfanwy Evans (University of Potsdam) DTSTART:20210617T143000Z DTEND:20210617T150000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/17 DESCRIPTION:Title: Triply-periodic tangling\nby Myfanwy Evans (University of Potsdam) as part of BIRS workshop : Novel Mathematical Methods in Materia l Science: Applications to Biomaterials\n\n\nAbstract\nUsing periodic surf aces as a scaffold is a convenient route to making periodic entanglements. I will present a systematic way of building new tangled periodic structu res\, using low-dimensional topology and combinatorics\, posing the questi on of how to characterise the structures more completely.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Elisabetta Matsumoto (Georgia Tech) DTSTART:20210617T150000Z DTEND:20210617T153000Z DTSTAMP:20260404T041200Z 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://stable.researchseminars.org/talk/BIRS_21w5232/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Radmila Sazdanovic (NC State University) DTSTART:20210617T154500Z DTEND:20210617T161500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/19 DESCRIPTION:Title: TDA applications in cancer genomics\nby Radmila Sazdanovi c (NC State University) as part of BIRS workshop : Novel Mathematical Meth ods in Material Science: Applications to Biomaterials\n\n\nAbstract\nCance r is a polygenic disease in which genomic events are selected in order to produce a sophisticated and coordinated outcome. Determining when two even ts are co-occurring is at the heart of finding possible genetic treatments and also an important open question in data science. This work focuses on further analysis and modification of the existing topological data analys is approach to breast cancer data. In particular we will address the stabi lity of proposed methods and possible generalizations to other contexts.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Harris (NC State University) DTSTART:20210617T161500Z DTEND:20210617T164500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/20 DESCRIPTION:Title: Multiscale Simulations of Biological Polymers\nby Sarah H arris (NC State University) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nP olymeric structures are ubiquitous in biology\, and perform diverse functi ons at multiple length-scales. DNA carries the genetic code through the c hemistry of the constituent bases at an atomic level\, but also plays an a ctive role in its own regulation through its ability to store and transmit mechanical stress over genomic length-scales. Long polymeric coiled-coils are a common protein structural motif\, and as well as forming the basis of robust super-macromolecular hierarchical structures such as collagen\, also have an active role in regulating the chemo-mechanical cycle of mole cular motors such as dynein and myosin. Intrinsically disordered proteins present a particular enigma\; some undergo disorder to order transitions o n encountering their binding partner and so participate in highly specific molecular recognition in spite of their apparent lack of structure\, wher eas others appear to generate vital emergent behaviour over far longer len gth-scales than their own structure\, such as the self-assembly of membran eless organelles.\nHere I will compare and contrast multi-scale representa tions of polymeric biomacromolecules from the fully atomistic up to the co ntinuum level. I will discuss open challenges to development and biologica l questions that would benefit from robust mathematical and computational models of biological polymers.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Rawdon (University of Saint Thomas) DTSTART:20210618T143000Z DTEND:20210618T150000Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/21 DESCRIPTION:Title: Accumulated knot probability\nby Eric Rawdon (University of Saint Thomas) as part of BIRS workshop : Novel Mathematical Methods in Material Science: Applications to Biomaterials\n\n\nAbstract\nMany knots i n nature are open knots\, not the closed knots from knot theory. There ar e several definitions of knotting in open curves\, each of which have thei r own advantages and disadvantages. The speaker's favorite open knot defi nition involves extending rays to infinity in a common direction from the endpoints 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\, the re is a knot type that appears in over 50% of the closure directions\, in which case we might all be able to agree that the open knot has the essenc e of that closed knot type. However\, there are many cases where there is no knot type that appears in over 50% of the closure directions\, especia lly near transitions between different knot types. We present the accumul ated knot probability as a way of making sense of these more ambiguous sit uations. The short story is that\, for a given knot type K\, we compute t he probability that the closures are a knot type which "includes" K in som e sense. In this talk\, we use the partial ordering on knots developed by Diao\, Ernst\, and Stasiak based on crossing changes in minimal knot diag rams\, which creates a sort of family tree of knots. However\, any sort o f family tree could be substituted here depending on what one is trying to model. We show how some of the knotting classifications change for some proteins and tight knot configurations.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Pei Liu (University of Minnesota) DTSTART:20210618T150000Z DTEND:20210618T153000Z DTSTAMP:20260404T041200Z 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://stable.researchseminars.org/talk/BIRS_21w5232/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Kenneth Millett (University of California\, Santa Barbara) DTSTART:20210618T154500Z DTEND:20210618T161500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/23 DESCRIPTION:Title: Using the HOMFLY-PT polynomial to quantuantify the entangleme nt of collections of open chains\nby Kenneth Millett (University of Ca lifornia\, Santa Barbara) as part of BIRS workshop : Novel Mathematical Me thods in Material Science: Applications to Biomaterials\n\n\nAbstract\nThe superposition of HOMFLY-PT polynomials of collections of open chains prov ides an "average" of the\npolynomials associated to individual closures an d\, consequently\, a HOMFLY-PT polynomial for the open\nlink. Following a bri\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Rechnitzer (University of California\, Santa Barbara) DTSTART:20210618T161500Z DTEND:20210618T164500Z DTSTAMP:20260404T041200Z UID:BIRS_21w5232/24 DESCRIPTION:Title: Trials and tribulations of preserving topology\nby Andrew Rechnitzer (University of California\, Santa Barbara) as part of BIRS wor kshop : Novel Mathematical Methods in Material Science: Applications to Bi omaterials\n\n\nAbstract\nMonte Carlo simulations are a big part of unders tanding the statistical properties of knots. Unfortunately\, if one wishes to study curves of fixed knot types then there are very few methods avail able. This work\, with Nick Beaton and Nathan Clisby\, is an attempt to ad apt existing algorithms to polygons in R3 of fixed topology. It is very mu ch a work in progress\, but I will report on our work adapting BFACF to po lygons in R3\, and also our attempts at trying to coerce the (very fast) p ivot algorithm to respect topology.\n LOCATION:https://stable.researchseminars.org/talk/BIRS_21w5232/24/ END:VEVENT END:VCALENDAR