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DTSTART;TZID=America/Los_Angeles:20191001T121500
DTEND;TZID=America/Los_Angeles:20191001T131000
DTSTAMP:20260430T102452
CREATED:20190824T031500Z
LAST-MODIFIED:20191001T150201Z
UID:1368-1569932100-1569935400@colleges.claremont.edu
SUMMARY:Combinatorics and representation theory of Temperley-Lieb algebras (Zajj Daugherty\, CUNY)
DESCRIPTION:The classical\, one-boundary\, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as “diagram algebras”\, meaning that they have basis elements depicted as certain kinds of graphs\, and multiplication rules are given by stacking diagrams and gluing of vertices. In this talk\, we will explore these algebras and their representation theory\, as well as their relationship to other important diagram algebras in combinatorial representation theory.
URL:https://colleges.claremont.edu/ccms/event/anct-seminar-zajj-daugherty-cuny/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
GEO:34.099908;-117.7142522
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191001T150000
DTEND;TZID=America/Los_Angeles:20191001T160000
DTSTAMP:20260430T102452
CREATED:20190825T192823Z
LAST-MODIFIED:20190906T223333Z
UID:1372-1569942000-1569945600@colleges.claremont.edu
SUMMARY:Topology Seminar: Jesse Levitt (USC)
DESCRIPTION:Title: Understanding Structure in the Single Variable Knot Polynomials \nAbstract: \nWe examine the dimensionality and internal structure of the aggregated data produced by the Alexander\, Jones\, and Z0 polynomials using topological data analysis and dimensional reduction techniques. By examining several families of knots\, including over 10 million distinct examples\, we find that the Jones data is well described as a three dimensional manifold\, the Z0 data as a single two dimensional manifold and the Alexander data as a collection of two dimensional manifolds. We confirm each of these structural results using two independent ‘big data’ techniques. The ability to consider knots in this manner illuminates several interesting relationships that I hope to discuss at the conclusion of the talk. This collects joint work with Mustafa Hajij and Radmila Sazdanovic.
URL:https://colleges.claremont.edu/ccms/event/topology-seminar-jesse-levitt-usc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Topology Seminar
ORGANIZER;CN="Sam Nelson":MAILTO:snelson@cmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191002T161500
DTEND;TZID=America/Los_Angeles:20191002T171500
DTSTAMP:20260430T102452
CREATED:20190826T234640Z
LAST-MODIFIED:20190928T054259Z
UID:1390-1570032900-1570036500@colleges.claremont.edu
SUMMARY:Freeways and Circle Packing
DESCRIPTION:The beauty of mathematics is often encountered when one discovers that two apparently very different phenomena actually share a common origin. I will discuss such a surprising connection between two apparently unrelated mathematical objects. One is purely combinatorial: the number of ways one can drive from USC to the Claremont Colleges. The other one is geometric: the Ford circle packing\, a pretty configuration of circles in the plane with interesting number theoretic properties.
URL:https://colleges.claremont.edu/ccms/event/tba-6/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
GEO:34.0999157;-117.7142668
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191004T160000
DTEND;TZID=America/Los_Angeles:20191004T170000
DTSTAMP:20260430T102452
CREATED:20190808T233920Z
LAST-MODIFIED:20190919T220053Z
UID:1353-1570204800-1570208400@colleges.claremont.edu
SUMMARY:Regime transitions of liquid films flowing down a fiber (Applied Math Talk given by Prof. Claudia Falcon\, UCLA)
DESCRIPTION:Recent  experiments  of  thin  films  flowing  down  a  vertical  fiber  with  varying  nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. Determining  the  regime  transitions from absolute (Rayleigh- Plateau) instability is useful in the  design  of  heat  and  mass  exchangers for applications that include cooling systems and desalination. We present a detailed analysis using a full lubrication model that includes slip boundary conditions\, nonlinear curvature terms\, and a film stabilization term. This study brings to focus the presence of a stable liquid layer playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity  and  stability  of  traveling  droplets  in  the  experiments  and their  transition  to isolated droplets. When thermal gradients are present\, it can induce bead coalescence away from the nozzle. To account for this\, we incorporate spatial-dependent viscosity and surface tension to the model\, due  to  inhomogeneous  temperature  field  along  the  fiber.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-prof-claudia-falcon/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
GEO:34.099908;-117.7142522
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Emmy Noether Room Millikan 1021 Pomona College 610 N. College Ave. Claremont California 91711;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142522,34.099908
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191005T100000
DTEND;TZID=America/Los_Angeles:20191005T120000
DTSTAMP:20260430T102452
CREATED:20190913T171044Z
LAST-MODIFIED:20190913T171044Z
UID:1541-1570269600-1570276800@colleges.claremont.edu
SUMMARY:GEMS Workshop: Symmetry with Professor Michael Orrison\, from Harvey Mudd College
DESCRIPTION:TOPIC: Symmetry \nSymmetry seems to be an important idea in mathematics\, but how do mathematicians think about symmetry? In this workshop\, we’ll talk about mathematical objects called groups\, see how they are used to describe symmetry\, and then put them to work to help us answer some nontrivial counting problems. \nWHAT IS GEMS: \nThe Gateway to Exploring Mathematics program (GEMS) is a series of workshops that helps excite the interests and curiosity of young students in mathematics and science. \nGEMS meets once a month on a Saturday morning from 10:00 AM to 12:00 PM. \nGEMS is designed to reach 8th\, 9th and 10th grade students who have an interest in mathematics and science. \nParticipants interact with excellent and award winning faculty\, staff\, students and alumni from each of the seven Claremont Colleges. \nFALL 2019 DATES: \nOctober 5\, 2019 \nNovember 2\, 2019 \nDecember 7\, 2019 \nREGISTRATION: \nTo register for our next event on October 5\, please click on the following link: \nhttps://forms.gle/LySNdhqj782TkPFz9 \nANY QUESTIONS: \nPlease contact our 2019-2020 GEMS coordinator\, Josh Kiernan at joshua.kiernan@cgu.edu
URL:https://colleges.claremont.edu/ccms/event/gems-workshop-symmetry-with-professor-michael-orrison-from-harvey-mudd-college/
LOCATION:Shanahan 1480\, Harvey Mudd College\, 301 Platt Blvd.\, Claremont\, CA\, 91711\, United States
CATEGORIES:GEMS
ORGANIZER;CN="Josh Kiernan":MAILTO:joshua.kiernan@cgu.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191007T163000
DTEND;TZID=America/Los_Angeles:20191007T173000
DTSTAMP:20260430T102452
CREATED:20190911T040840Z
LAST-MODIFIED:20190930T185051Z
UID:1528-1570465800-1570469400@colleges.claremont.edu
SUMMARY:Applied Math Seminar: Mathematical model of Hematopoietic cell differentiation from single-cell gene sequencing data (Prof. Heyrim Cho \,UCR)
DESCRIPTION:Recent advances in single-cell gene sequencing data and high-dimensional data analysis techniques are bringing in new opportunities in modeling biological systems. In this talk\, I will discuss different approaches to develop mathematical models from single-cell data. Particularly for high-dimensional single-cell gene sequencing data\, dimension reduction techniques are applied to find the trajectories of cell states in the reduced differentiation space. Then\, we develop PDE models that describe the cell differentiation as directed and random movement on the abstracted graph or on the reduced space. Normal hematopoiesis differentiation and abnormal processes of acute myeloid leukemia (AML) progression are simulated\, and the model can predict the emergence of cells in novel intermediate states of differentiation consistent with immunophenotypic characterizations of AML. In addition\, we demonstrate that our model is capable to illustrate the reconstitution of impaired Hematopoiesis\, for instance\, after chemotherapy.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-prof-heyrim-cho-ucr/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
GEO:34.099908;-117.7142522
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Emmy Noether Room Millikan 1021 Pomona College 610 N. College Ave. Claremont California 91711;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142522,34.099908
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191008T121500
DTEND;TZID=America/Los_Angeles:20191008T131000
DTSTAMP:20260430T102452
CREATED:20190909T203312Z
LAST-MODIFIED:20190909T203312Z
UID:1495-1570536900-1570540200@colleges.claremont.edu
SUMMARY:Matroids: a unified theory of independence (Mauricio Gomez Lopez\, University of Oregon)
DESCRIPTION:In this talk\, I will give an overview of the theory of matroids. These are mathematical objects which capture the combinatorial essence of linear independence. Besides providing some basic definitions of this theory\, I will discuss several examples of matroids and explain some connections with optimization. Also\, in this talk\, I will introduce matroid polytopes\, which provide a geometric framework for studying matroids. If time permits\, I will discuss some new proofs to known results that I developed with one of my students during a research program this summer.
URL:https://colleges.claremont.edu/ccms/event/matroids-a-unified-theory-of-independence-mauricio-gomez-lopez-university-of-oregon/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
GEO:34.099908;-117.7142522
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Emmy Noether Room Millikan 1021 Pomona College 610 N. College Ave. Claremont California 91711;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142522,34.099908
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191008T150000
DTEND;TZID=America/Los_Angeles:20191008T160000
DTSTAMP:20260430T102452
CREATED:20190909T230001Z
LAST-MODIFIED:20190919T032450Z
UID:1499-1570546800-1570550400@colleges.claremont.edu
SUMMARY:Topology Seminar: Mauricio Gomez Lopez (U. Oregon)
DESCRIPTION:Title: Cobordism Categories and Spaces of Manifolds. \nAbstract: Cobordisms have been one of the central objects in topology since the pioneering work of Rene Thom\, which provided the first link between manifolds and homotopy theory. In more recent years\, there has been much focus on cobordism categories. These play a fundamental role in the study of topological quantum field theories and automorphism groups of manifolds.  A fundamental result in this field is the theorem of Galatius\, Madsen\, Tillmann\, and Weiss\, which describes the homotopy type of the classifying spaces of smooth cobordism categories. Galatius and Randal-Williams later simplified the proof of this result with the use of spaces of manifolds and scanning techniques. Besides giving an overview of this field of research\, I will discuss the analogs of the theorem of Galatius\, Madsen\, Tillmann\, and Weiss for topological and PL manifolds. The topological case is joint work with Alexander Kupers.
URL:https://colleges.claremont.edu/ccms/event/topology-seminar-mauricio-gomez-lopez-u-oregon/
LOCATION:CA
CATEGORIES:Topology Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191009T161500
DTEND;TZID=America/Los_Angeles:20191009T171500
DTSTAMP:20260430T102452
CREATED:20190826T234829Z
LAST-MODIFIED:20191004T182414Z
UID:1392-1570637700-1570641300@colleges.claremont.edu
SUMMARY:Formal geometry and characteristic classes
DESCRIPTION:I plan to explain how a purely algebraic technique involving Lie Algebra Cohomology can be used to construct standard characteristic classes of vector bundles and foliations (in fact\, it could be tweaked to give most characteristic classes in differential and complex geometry).
URL:https://colleges.claremont.edu/ccms/event/tba-7/
LOCATION:CA
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191014T161500
DTEND;TZID=America/Los_Angeles:20191014T171500
DTSTAMP:20260430T102452
CREATED:20190911T055121Z
LAST-MODIFIED:20190919T171212Z
UID:1530-1571069700-1571073300@colleges.claremont.edu
SUMMARY:Applied Math Talk: A Full Asymptotic Series of European Call Option Prices in the SABR Model with Beta = 1 given by Zhengji Guo (CGU)
DESCRIPTION:We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model\, as well as improve the speed of the calculations. We consider the SABR model (with $\beta=1$) of stochastic volatility\, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al (2006) who showed that under stochastic volatility framework\, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term\, by using the conditional density of the average volatility\, and write it as a two-dimensional integral. For the correction part\, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin\, Peng\, and Schellhorn (2016) with analytical calculations. The first approach\, which we call ”Dyson series on the return’s idiosyncratic noise” yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor’s (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion. The second approach\, which we call ”Dyson series on the common noise” necessitates the calculation of only a one-dimensional integral\, but the formula is more complex. This research consisted of both analytical derivations and numerical calculations. The latter show that our formulae are in general more exact\, yet more time-consuming to calculate\, than the first order expansion of Hagan et al (2002).
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-zhengji-guo-cgu/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Applied Math Seminar
GEO:34.099908;-117.7142522
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Emmy Noether Room Millikan 1021 Pomona College 610 N. College Ave. Claremont California 91711;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142522,34.099908
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191015T121500
DTEND;TZID=America/Los_Angeles:20191015T131000
DTSTAMP:20260430T102452
CREATED:20190830T203403Z
LAST-MODIFIED:20191010T171535Z
UID:1465-1571141700-1571145000@colleges.claremont.edu
SUMMARY:Sporadic points on modular curves (Ozlem Ejder\, Colorado State University)
DESCRIPTION:A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular\, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are moduli spaces for elliptic curves with an additional structure.  In particular\, $X_1(n)$ classifies the elliptic curves with a point of order of $n$.  Motivated by the classification of torsion problems\, we study the sporadic points on the curve $X_1(n)$\, that is\, the closed points on $X_1(n)$ such that there are at most finitely many points of degree at most $\deg(x)$. In this talk\, we will discuss the finiteness of sporadic points. This is joint with A. Bourdon\, Y. Liu\, F. Odumudu and B. Viray.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-ozlem-ejder-colorado-state-university/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
GEO:34.099908;-117.7142522
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Emmy Noether Room Millikan 1021 Pomona College 610 N. College Ave. Claremont California 91711;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142522,34.099908
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191016T161500
DTEND;TZID=America/Los_Angeles:20191016T171500
DTSTAMP:20260430T102452
CREATED:20190826T234917Z
LAST-MODIFIED:20191007T175651Z
UID:1394-1571242500-1571246100@colleges.claremont.edu
SUMMARY:Habitat-driven extinctions: insights from spatially implicit ODE models 
DESCRIPTION:Speaker:  Kate Meyer\, Cornell University\n\n\n\n\n\n\n\n\n\nAbstract: Biodiversity underpins ecosystem functioning but continues to decline on a global scale. Among human activities driving this trend\, habitat destruction is a leading culprit in local and global extinctions. Simple mathematical models can address important questions surrounding habitat-driven extinctions—for example\, which species are at highest risk\, how delayed might extinction be\, and what can be done about it? Exploring these questions in a spatially implicit ODE model leads us to new mathematical territory involving temporary parameter changes and nonequilibrium dynamics.\n\n\n\nHost: Jasper Weinburd (jweinburd@hmc.edu)
URL:https://colleges.claremont.edu/ccms/event/tba-8/
LOCATION:CA
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191021T161500
DTEND;TZID=America/Los_Angeles:20191021T171500
DTSTAMP:20260430T102452
CREATED:20190705T211849Z
LAST-MODIFIED:20191018T203146Z
UID:1337-1571674500-1571678100@colleges.claremont.edu
SUMMARY:Applied Math Talk: Dynamics of neuroendocrine stress response given by Prof. Maria Rita D'Orsogna (CSUN)
DESCRIPTION:The hypothalamic-pituitary-adrenal (HPA) axis is a neuroendocrine system\nthat regulates numerous physiological processes. Disruptions are\ncorrelated with stress-related diseases such as PTSD and major depression. We characterize “normal” and “diseased” states of the HPA axis as basins of attraction of a dynamical system describing the main hormones regulated by the HPA axis. Our model includes hormonal self-upregulation\, release\, synthesis; interaction\,\ndelay and feedback mechanisms. External input is associated to psychological trauma\, while parameter changes represent physiological damage. We show that transitions between the  “normal” and “diseased” states may be induced solely by\nexternal input\, with all physiological parameters unchanged\, emphasizing\nthe severe consequences of psychological trauma. We also find that the\ntiming and duration of the traumatic event is an important determinant\nof if and how stress disorders will manifest. Finally\, we propose mechanisms whereby exposure therapy may act to normalize downstream dysregulation of the HPA axis.
URL:https://colleges.claremont.edu/ccms/event/applied-math-talk-given-by-prof-maria-rita-dorsogna-csun/
LOCATION:CGU Math North House
CATEGORIES:Applied Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191023T161500
DTEND;TZID=America/Los_Angeles:20191023T171500
DTSTAMP:20260430T102452
CREATED:20190826T235239Z
LAST-MODIFIED:20191018T182721Z
UID:1396-1571847300-1571850900@colleges.claremont.edu
SUMMARY:Magnitude meets persistence. What happens after?
DESCRIPTION:The magnitude is an isometric invariant of metric spaces that\nwas introduced by Tom Leinster in 2010\, and is currently the object of\nintense research\, as it has been shown to encode many invariants of a\nmetric space such as volume\, dimension\, and capacity. When studying a\nmetric space in topological data analysis using persistent homology\, one\napproximates the space through a nested sequence of simplicial complexes\nso as to recover topological information about the space by studying the\nhomology of this sequence. In this talk I will give an introduction to\nmagnitude as well as persistent homology\, and explain how magnitude\nhomology is related to persistent homology.
URL:https://colleges.claremont.edu/ccms/event/tba-9/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
GEO:34.0999157;-117.7142668
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Argue Auditorium Pomona College 610 N. College Ave. Claremont CA 91711 United States;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142668,34.0999157
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191029T121500
DTEND;TZID=America/Los_Angeles:20191029T131000
DTSTAMP:20260430T102452
CREATED:20190802T043328Z
LAST-MODIFIED:20190903T050156Z
UID:1347-1572351300-1572354600@colleges.claremont.edu
SUMMARY:Faster point counting for curves over prime power rings (Maurice Rojas\, Texas A&M)
DESCRIPTION:Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology\, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization is to count the number of points over prime power rings\, e.g.\, the integers modulo a prime power. However\, the theory behind the latter kind of point counting began more recently and there are numerous gaps in our algorithmic knowledge. \nWe give a simple combinatorial construction that reduces point counting over prime power point counting to the prime field case. In particular\, for any bivariate polynomial f in Z[x\,y] and positive integers p and k with p prime\, we show how one can count the number of roots of f in (Z/(p^k))^2 in time p^{1/2 + o(1)} (dk)^{O(1)}\, and even faster for certain curves. This generalizes earlier results of Cheng\, Lecerf\, Saxena\, and Wan in the univariate case\, and simplifies earlier work of Denef\, Igusa\, and Veys on local zeta functions. \nThis is joint work with Caleb Robelle and Yuyu Zhu.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-maurice-rojas-texas-am/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
GEO:34.099908;-117.7142522
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Emmy Noether Room Millikan 1021 Pomona College 610 N. College Ave. Claremont California 91711;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142522,34.099908
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191030T161500
DTEND;TZID=America/Los_Angeles:20191030T171500
DTSTAMP:20260430T102452
CREATED:20190826T235343Z
LAST-MODIFIED:20191025T235302Z
UID:1398-1572452100-1572455700@colleges.claremont.edu
SUMMARY:Calculus\, Real Fewnomials\, and P vs NP
DESCRIPTION:We review a beautiful 17th century result by the philosopher Rene Descartes: a univariate real polynomial with t monomial terms has no more than t-1 positive roots. We then see how one can prove a generalization that counts roots of two bivariate polynomials (with few monomial terms)\, using nothing more than basic calculus. In other words\, we’ll see the basics of real fewnomial theory. We’ll then see how this relates to circuit complexity and the famous P vs. NP Problem. In particular\, we’ll see how new bounds in real fewnomial theory lead to new separations of complexity classes that answer deep questions in theoretical computer science. Along the way\, we’ll see some of the ideas behind tropical geometry.
URL:https://colleges.claremont.edu/ccms/event/tba-10/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Blerta Shtylla":MAILTO:shtyllab@pomona.edu
GEO:34.0999157;-117.7142668
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Argue Auditorium Pomona College 610 N. College Ave. Claremont CA 91711 United States;X-APPLE-RADIUS=500;X-TITLE=610 N. College Ave.:geo:-117.7142668,34.0999157
END:VEVENT
END:VCALENDAR