BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Mathematical Sciences - ECPv6.15.18//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-ORIGINAL-URL:/math X-WR-CALDESC:Events for Mathematical Sciences REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:America/Chicago BEGIN:DAYLIGHT TZOFFSETFROM:-0600 TZOFFSETTO:-0500 TZNAME:CDT DTSTART:20230312T080000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0500 TZOFFSETTO:-0600 TZNAME:CST DTSTART:20231105T070000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0600 TZOFFSETTO:-0500 TZNAME:CDT DTSTART:20240310T080000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0500 TZOFFSETTO:-0600 TZNAME:CST DTSTART:20241103T070000 END:STANDARD BEGIN:DAYLIGHT TZOFFSETFROM:-0600 TZOFFSETTO:-0500 TZNAME:CDT DTSTART:20250309T080000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:-0500 TZOFFSETTO:-0600 TZNAME:CST DTSTART:20251102T070000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240202T140000 DTEND;TZID=America/Chicago:20240202T153000 DTSTAMP:20260423T063830 CREATED:20240125T214400Z LAST-MODIFIED:20240125T214400Z UID:10016133-1706882400-1706887800@uwm.edu SUMMARY:Colloquium: Dr. Eva Goedhart DESCRIPTION:A Tree Approach to Solving Diophantine Equations\nDr. Eva Goaedhart\nVisiting Scholar\nFranklin & Marshall College \nDiophantine equations are easy to state equations that often require complicated tools to solve. After introducing Diophantine equations\, I will present a visual approach to solving a family of Diophantine equations. URL:/math/event/colloquium-dr-eva-goedhart/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240209T123000 DTEND;TZID=America/Chicago:20240209T133000 DTSTAMP:20260423T063830 CREATED:20240205T160808Z LAST-MODIFIED:20240205T160935Z UID:10016134-1707481800-1707485400@uwm.edu SUMMARY:Graduate Student Colloquium: Mrs. Kelsey Brouwer DESCRIPTION:Julia Sets in Parameter Space for the Generalized McMullen Map\nMrs. Kelsey Brouwer\nPhD Student\nUniversity of Wisconsin – Milwaukee \nWe will begin by introducing the field of complex dynamics and explaining the two types of pictures that dynamicists are interested in\, namely Julia sets and parameter spaces. Next\, we’ll introduce the generalized McMullen map and share some results about its Julia sets and parameter spaces. Finally\, we will demonstrate an interesting connection between McMullen parameter space and quadratic Julia sets and discuss some potential techniques for explaining and documenting this phenomenon. A software demonstration may follow. URL:/math/event/graduate-student-colloquium-mrs-kelsey-brouwer/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240216T123000 DTEND;TZID=America/Chicago:20240216T133000 DTSTAMP:20260423T063830 CREATED:20240212T152852Z LAST-MODIFIED:20240212T152852Z UID:10016136-1708086600-1708090200@uwm.edu SUMMARY:Graduate Student Colloquium: Mr. Joe Paulson DESCRIPTION:Introduction to Topological Combinatorics\nMr. Joe Paulson\nPhD Student\nUniversity of Wisconsin – Milwaukee \nWith the prominence of topology and combinatorics at 51\, we’ll explore the intersection of these fields. This relatively new field originated with the solving of Kneser’s conjecture via Lovasz’s use of topological methods. We’ll explore Lovasz’s solution and other solutions to famous problems such as the Necklace problem and the Inscribed Rectangle. URL:/math/event/graduate-student-colloquium-mr-joe-paulson-2/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240216T140000 DTEND;TZID=America/Chicago:20240216T150000 DTSTAMP:20260423T063830 CREATED:20240208T212115Z LAST-MODIFIED:20240208T212115Z UID:10016135-1708092000-1708095600@uwm.edu SUMMARY:Colloquium: Dr. Bogdan Nica DESCRIPTION:Elementary Matrix Operations on a Napkin\nDr. Bogdan Nica\nAssistant Professor\nIndiana University – Purdue University Indianapolis \nAtmospheric science provides excellent opportunities for encouraging student interest in all fields of STEM (Science\, Technology\, Engineering\, Math). A model outreach program (“Chasing the Wind: Tools for Understanding the Weather”) will be presented for use in elementary\, middle and high school classrooms. Key elements of the presentation will be highlighted: sharing of personal career background; story-telling about scientists and scientific concepts; utilization of physical props and humor; messaging on the importance of fluency in mathematics\, the language of STEM; and direct involvement of the audience. URL:/math/event/colloquium-dr-bogdan-nica/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240223T123000 DTEND;TZID=America/Chicago:20240223T133000 DTSTAMP:20260423T063830 CREATED:20240219T151918Z LAST-MODIFIED:20240219T154130Z UID:10016145-1708691400-1708695000@uwm.edu SUMMARY:Graduate Student Colloquium: Mr. Joakim Jakovleski DESCRIPTION:Representations of the Natural Numbers Using Box Arrangements\nMr. Joakim Jakovleski\nPhD Student\nUniversity of Wisconsin – Milwaukee \nNatural numbers can be presented as sums of numbers in boxes\, where we are subject to certain rules about how we generate the boxes and the numbers in them. In this talk\, we will explore this presentation and investigate the properties of boxes of different sizes. We will center on a simplified way to obtain all numbers in all boxes using a certain subset of them\, and use it to ultimately produce a formula for these numbers. We then manage to provide some generalizations\, and pave the field for potential future work. URL:/math/event/graduate-student-colloquium-mr-joakim-jakovleski/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240301T123000 DTEND;TZID=America/Chicago:20240301T133000 DTSTAMP:20260423T063830 CREATED:20240226T151035Z LAST-MODIFIED:20240226T151307Z UID:10016146-1709296200-1709299800@uwm.edu SUMMARY:Graduate Student Colloquium: Mr. John Museus DESCRIPTION:Games\, Winning\, and Nimbers\nMr. John Museus\nPhD Student\nUniversity of Wisconsin – Milwaukee \nThe Nimbers are a particularly peculiar Field which arises naturally when studying the winning strategies of Impartial Games. In this talk\, we will give a brief overview of the constructions leading up to the Nimbers by studying three games: Nim\, Subtraction\, and Turning Corners. Along the way we will see what Tweedledee and Tweedledum have to do with winning games and give an airtight proof that 2 tims 2 is actually 3. URL:/math/event/graduate-student-colloquium-mr-john-museus/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240301T140000 DTEND;TZID=America/Chicago:20240301T150000 DTSTAMP:20260423T063830 CREATED:20240213T184338Z LAST-MODIFIED:20240219T143038Z UID:10016137-1709301600-1709305200@uwm.edu SUMMARY:Colloquium : Dr. Selvi Kara DESCRIPTION:Combinatorial Resolutions of Monomial Ideals\nDr. Selvi Kara\nAssistant Professor of Mathematics\nBryn Mawr College \nOne of the central problems in commutative algebra concerns understanding the structure of an ideal in a polynomial ring. Abstractly\, an ideal’s structure can be expressed through an object called its minimal resolution\, but there is no explicit method to obtain a minimal resolution in general\, even for the simpler and fundamental class known as monomial ideals. \nIn this talk\, we will focus on resolutions of monomial ideals. In particular\, I will introduce a new combinatorial method that provides a resolution of any monomial ideal using tools from discrete Morse theory. URL:/math/event/colloquium-dr-selvi-kara/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240308T123000 DTEND;TZID=America/Chicago:20240308T133000 DTSTAMP:20260423T063830 CREATED:20240304T180710Z LAST-MODIFIED:20240304T180849Z UID:10016147-1709901000-1709904600@uwm.edu SUMMARY:Graduate Student Colloquium: Dorian Smith DESCRIPTION:Sandpile Group For Cones Over Trees\nDorian Smith\nPhD Student\nUniversity of Minnesota Twin Cities \nThe sandpile group $K(G)$ of a graph $G$ is a finite abelian group\, isomorphic to the cokernel of the reduced graph Laplacian of $G.$ We study $K(G)$ when $G = Cone(T)$. The graph $Cone(T)$ is obtained from a tree $T$ on $n$ vertices by attaching a new cone vertex attached to all other vertices. For two such families of graphs\, we will describe $K(G)$ exactly: the fan graphs $Cone(P_n)$ where $P_n$ is a path\, and the thagomizer graph $Cone(S_n)$ where $S_n$ is the star-shaped tree. The motivation is that these two families turn out to be extreme cases among $Cone(T)$ for all trees $T$ on $n$ vertices. URL:/math/event/graduate-student-colloquium-dorian-smith/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240308T140000 DTEND;TZID=America/Chicago:20240308T150000 DTSTAMP:20260423T063830 CREATED:20240213T184556Z LAST-MODIFIED:20240229T211321Z UID:10016138-1709906400-1709910000@uwm.edu SUMMARY:Colloquium: Dr. Emmanuel Asante-Asamani DESCRIPTION:A Mechanochemical Model of Cell Migration in Confined Environments\nDr. Emmanuel Asante-Asamani\nAssistant Professor of Mathematics\nClarkson University \nEukaryotic cells can move in confined environments by using pressure driven protrusions of their cell membrane\, a motility mechanism known as blebbing. Blebbing has been observed to facilitate the movement of tumor cells and some cancer cells during metastasis. Many questions remain unanswered about how cells translate mechanical cues from their environment into coordinated movement during blebbing. Of particular interest is how proteins that link the cell membrane to the cortex regulate the size and frequency of blebs under different levels of environmental confinement. In this talk\, I will present a multiscale model of bleb expansion that treats the cell as a viscous fluid encased by a viscoelastic boundary\, whose mechanical properties are regulated by dynamic structural and motor proteins. Numerical simulation of this model supports experimental data suggesting\, contrary to intuition\, that weakening the adhesion of the cell membrane to the cortex produces smaller and less frequent blebs. URL:/math/event/colloquium-dr-emmanuel-asante-asamani/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240315T123000 DTEND;TZID=America/Chicago:20240315T133000 DTSTAMP:20260423T063830 CREATED:20240311T171530Z LAST-MODIFIED:20240311T172157Z UID:10016148-1710505800-1710509400@uwm.edu SUMMARY:Graduate Student Colloquium: Dorian Smith DESCRIPTION:On the Lucky and Displacement Statistics of Stirling Permutations\nDorian Smith\nPhD Student\nUniversity of Minnesota Twin Cities \nStirling permutations are parking functions. We investigate two parking function statistics in the context of these objects: lucky cars and displacement. Among our results\, we consider two extreme cases: extremely lucky Stirling permutations (those with maximally many lucky cars) and extremely unlucky Stirling permutations (those with exactly one lucky car). We show that the number of extremely lucky Stirling permutations of order n is the Catalan number\, and the number of extremely unlucky Stirling permutations is (n−1)!. \nThis is a joint work with Laura Colmenarejo\, Aleyah Dawkins\, Jennifer Elder\, Pamela E. Harris\, Kimberly J.Harry\, Selvi Kara\, and Bridget Eileen Tenner. URL:/math/event/graduate-student-colloquium-dorian-smith-2/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240315T140000 DTEND;TZID=America/Chicago:20240315T150000 DTSTAMP:20260423T063830 CREATED:20240213T184840Z LAST-MODIFIED:20240311T132445Z UID:10016141-1710511200-1710514800@uwm.edu SUMMARY:Colloquium: Dr. Jean-Pierre Mutunguha DESCRIPTION:The Dynamical view of Free-by-Cyclic Groups\nDr. Jean Pierre Mutanguha\nInstructor\nPrinceton \nFree-by-cyclic groups can be defined as mapping tori of free group automorphisms. I will discuss various dynamical properties of automorphisms that turn out to be group invariants of the corresponding free-by-cyclic groups (e.g. growth type). In particular\, certain dynamical hierarchical decompositions of an automorphism determine canonical hierarchical decompositions of its mapping torus. URL:/math/event/colloquium-jean-pierre-mutunguha/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;VALUE=DATE:20240317 DTEND;VALUE=DATE:20240324 DTSTAMP:20260423T063830 CREATED:20240213T184658Z LAST-MODIFIED:20240213T184658Z UID:10016139-1710633600-1711238399@uwm.edu SUMMARY:Spring Break DESCRIPTION: URL:/math/event/spring-break/ X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240329T123000 DTEND;TZID=America/Chicago:20240329T133000 DTSTAMP:20260423T063830 CREATED:20240325T150400Z LAST-MODIFIED:20240325T150711Z UID:10016151-1711715400-1711719000@uwm.edu SUMMARY:Graduate Student Colloquium: Daniel Quigley DESCRIPTION:A Primer on the Mathematics of Artificial Neural Networks\nDaniel Quigley\nPhD Student\nUniversity of Wisconsin-Milwaukee \nArtificial neural networks (ANNs\, or\, simply\, neural networks) are ubiquitous\, not least of all in the context of modern machine learning. This presentation is a primer on the mathematics that underlie the mechanics of relatively simple feedforward ANNs. A sketch of the proof for the universal approximation theorem is given\, which states that a (fully connected) ANN with at least one hidden layer (of a sufficient number of neurons)\, together with a non-linear activation function\, can approximate any continuous function on a compact set to arbitrary accuracy. This presentation contributes to the movement for providing mathematical explanations and descriptions of ANNs\, favoring a functional analytical and well-founded framework at the expense of algorithmic aspects of deep learning otherwise concerned with identifying the most suitable deep ANNs for specific applications. URL:/math/event/graduate-student-colloquium-daniel-quigley/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240329T140000 DTEND;TZID=America/Chicago:20240329T150000 DTSTAMP:20260423T063830 CREATED:20240319T161218Z LAST-MODIFIED:20240319T161218Z UID:10016149-1711720800-1711724400@uwm.edu SUMMARY:Colloquium: Dr. Jay Pantone DESCRIPTION:Experimental Methods in Combinatorics\nDr. Jay Pantone\nAssistant Professor of Mathematics\nMarquette University \nWhat number comes next in the sequence\n1\, 2\, 4\, 8\, 16\, 32\, … ? \nHow about\n1\, 2\, 3\, 5\, 8\, 13\, … ? \nOr maybe\n1\, 3\, 14\, 84\, 592\, 4659\, … ? \nMany questions in combinatorics have the form “How many objects are there that have size n and that satisfy certain properties?” For example\, there are n! permutations (rearrangements) of n distinct objects\, there are 2^n binary strings of length n\, and the number of sequences of n coin flips that never have two tails in a row is the nth Fibonacci number. The “counting sequence” of a set of objects is the sequence a_0\, a_1\, a_2\, …\, where a_n is the number of objects of size n. \nAs a result of theoretical advances and more powerful computers\, it is becoming common to be able to compute a large number of initial terms of the counting sequence of a set of objects that you’d like to study. From these initial terms\, can you guess future terms? Can you guess a formula for the nth term in the sequence? Can you guess the asymptotic behavior as n tends to infinity? \nRigorously\, you can prove basically nothing from just some known initial terms. But\, perhaps surprisingly\, there are several empirical techniques that can use these initial terms to shed some light on the nature of a sequence. \nAs we talk about two such techniques — automated conjecturing of generating functions\, and the method of differential approximation — we’ll exhibit their usefulness through a variety of combinatorial topics\, including chord diagrams\, permutation classes\, and inversion sequences. URL:/math/event/colloquium-dr-jay-pantone/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240403T163000 DTEND;TZID=America/Chicago:20240403T173000 DTSTAMP:20260423T063830 CREATED:20240213T185431Z LAST-MODIFIED:20240328T192454Z UID:10016144-1712161800-1712165400@uwm.edu SUMMARY:Marden Lecture: Professor Caroline J Klivans DESCRIPTION:The intrigue that compels us \nWhen we witness unexpected phenomena\, a mathematician finds themselves asking: why?  We are compelled to understand further; what is the cause\, the basic underlying principles?   Mathematics is full of symmetries\, patterns and visuals that we can appreciate in their own right or use to explain and illustrate concepts.  And\, they can also drive us to discovery.  I will tell a story of chip-firing\, a mathematical idea that leads to fascinatingly intricate structures.  The imagery of these structures has spurred many questions to which we know surprisingly few answers.\n \n  URL:/math/event/marden-lecture-caroline-j-klivans/ LOCATION:Lubar Hall N140\, 3202 N Maryland Ave\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Marden Lecture Series ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240404T130000 DTEND;TZID=America/Chicago:20240404T140000 DTSTAMP:20260423T063830 CREATED:20240319T164958Z LAST-MODIFIED:20240325T151828Z UID:10016150-1712235600-1712239200@uwm.edu SUMMARY:Marden Special Topics Seminar: Prof. Caroline Klivans DESCRIPTION:The Mathematics of Chip-Firing\nCaroline Klivans\nProfessor of Applied Mathematics\, Deputy Director of ICERM\nBrown University \nChip-firing processes are discrete dynamical systems. A commodity (chips\, sand\, dollars) is exchanged between sites of a network according to simple local rules. Although governed by local rules\, the long-term global behavior of the system reveals unexpected properties\, including intricate fractal-like patterns. In this talk\, I will give a broad survey of the theory of chip-firing\, highlighting both classical results and recent advances. URL:/math/event/marden-special-topics-seminar/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Seminars ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240405T123000 DTEND;TZID=America/Chicago:20240405T133000 DTSTAMP:20260423T063830 CREATED:20240401T163151Z LAST-MODIFIED:20240401T163151Z UID:10016152-1712320200-1712323800@uwm.edu SUMMARY:Graduate Student Colloquium: Kimberly Hadaway DESCRIPTION:On Combinatorial Problems of Generalized Parking Functions\nKimberly Hadaway\nPhD Student\nIowa State University \nIn this talk\, we study combinatorial problems related to generalized parking functions. Our work is motivated by two different research questions posed to us by Dr. Ken Fan and Dr. Shanise Walker. First\, we reframe Dr. Fan’s probabilistic question in terms of defective parking functions\, which enumerate the number of cars unable to park in the classical parking function problem\, thereby providing a partial answer to his question. Second\, we answer Dr. Walker’s question establishing a bijection between unit interval parking functions and the Fubini rankings\, which get their name as they are enumerated by the Fubini numbers. URL:/math/event/graduate-student-colloquium-kimberly-hadaway/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240412T140000 DTEND;TZID=America/Chicago:20240412T150000 DTSTAMP:20260423T063830 CREATED:20240213T184928Z LAST-MODIFIED:20240411T200759Z UID:10016142-1712930400-1712934000@uwm.edu SUMMARY:Colloquium: Prof. Yoichiro Mori DESCRIPTION:Mathematical Modeling of Cell Volume Control and Electrolyte Balance\nProf. Yoichiro Mori\nProfessor of Mathematics\nUniversity of Pennsylvania \nElectrolyte and cell volume regulation is essential in physiological systems. Biophysical modeling in this area\, however\, has been relatively sparse. After a brief introduction to cell volume control and electrophysiology\, I will discuss the classical pump-leak model of electrolyte and cell volume control. It will be shown that thermodynamic considerations lead to a new perspective of cell volume control. This classical model will then be generalized to a model with spatial extent (a system of partial differential equations) modeling cell-level electrodiffusive and osmotic phenomena. A simplified version of this model will then be applied to study osmosis-driven cell movement. I will also touch upon tissue-level models of ionic electrodiffusion and osmotic water flow which we have developed to study certain pathophysiologies of the central nervous system. URL:/math/event/colloquium-yoichiro-mori/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240419T123000 DTEND;TZID=America/Chicago:20240419T133000 DTSTAMP:20260423T063830 CREATED:20240415T180913Z LAST-MODIFIED:20240415T180913Z UID:10016157-1713529800-1713533400@uwm.edu SUMMARY:Graduate Student Colloquium: Matt McClinton DESCRIPTION:Harmonize your Fractals\nMatt McClinton\nGraduate Student\nUniversity of Wisconsin-Milwaukee \nThe Sierpinski Gasket (SG) is a known fractal object. A simple observation shows that SG is path connected. Unfortunately\, the infinitely jagged structure of the Gasket prevents these paths from being differentiable. If only there existed a means of smoothing out SG into an object where continuous and differentiable paths existed between pairs of points. As a matter of fact there is! \nI will demonstrate the technique known as “minimizing the graph energy” as described in the late Robert Strichartz’s book “Differential Equations on Fractals”. This technique involves finding the solution to a system of equations where the solution produces a graph that has differentiable paths\, and even better satisfies the Laplacian. Using a homeomorphic mapping defined by Jun Kigami in 1989\, by finding the graph energy minimizing values on level sets of SG\, we produce a fractal object known as the Harmonic Sierpinski Gasket (HSG). \nThis talk is intended for those that are interested in analysis\, algebra\, combinatorics\, topology\, fractal geometry\, and/or graph theory. Any necessary background information will be provided during the talk\, and I will end with some open problems. URL:/math/event/graduate-student-colloquium-matt-mcclinton/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240423T130000 DTEND;TZID=America/Chicago:20240423T141500 DTSTAMP:20260423T063830 CREATED:20240411T201711Z LAST-MODIFIED:20240415T133746Z UID:10016154-1713877200-1713881700@uwm.edu SUMMARY:Colloquium: Prof. Roger Howe DESCRIPTION:Mathematics around the Heisenberg Group\nProf. Roger Howe\nProfessor Emeritus\nYale University \nIn the mid 1920s\, Werner Heisenberg formulated the CCR – canonical commutation relations – describing the relationship between the operations of measuring position and of measuring momentum of a particle in quantum mechanics. These have been fundamental to the later\, dramatically successful development of subatomic physics. Shortly after Heisenberg’s work\, Hermann Weyl pointed out that the CCR defined the relations of a Lie algebra\, whose associated group is a two-step nilpotent group with one dimensional center. Today\, this group (and its increasingly large set of cousins) is known as the “Heisenberg group”. Over the remainder of the 20th century\, appreciation grew of the fundamental role of the Heisenberg group in disparate mathematical topics\, including harmonic analysis\, partial differential equations\, invariant theory and representation theory\, in both finite and infinite dimensions. This talk will review and attempt to summarize some of the manifold connections between these topics that are mediated by the Heisenberg group URL:/math/event/colloquium-prof-roger-howe/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240426T100000 DTEND;TZID=America/Chicago:20240426T120000 DTSTAMP:20260423T063830 CREATED:20240411T201135Z LAST-MODIFIED:20240411T201135Z UID:10016153-1714125600-1714132800@uwm.edu SUMMARY:PhD Dissertation Defense: Mr. William Braubach DESCRIPTION:Coarse Homotopy Extension Property and its Applications\nMr. William Braubach\nUniversity of Wisconsin-Milwaukee \nA pair (X\, A) has the homotopy extension property if any homotopy of A can be extended to a homotopy of X. The main goal of this dissertation is to define a coarse analog of the homotopy extension property for coarse homotopies and prove coarse versions of results from algebraic topology involving this property.\nFirst\, we define a notion of a coarse adjunction metric for constructing coarse adjunction spaces. We use this to redefine coarse CW complexes and to construct a coarse version of the mapping cylinder. We then prove various pairs of spaces have the coarse homotopy extension property. In particular\, pairs of coarse CW complexes. We then prove results involving the coarse homotopy extension property\, leading to the result that a coarse map f from X into Y is a coarse homotopy equivalence if and only if the coarse mapping cylinder coarse deformation retracts onto its copy of X. We use this to prove our main result\, a coarse version of Whitehead’s Theorem: If a cellular coarse map f between coarse CW complexes induces isomorphisms between coarse homotopy groups\, then f is a coarse homotopy equivalence. \nAdvisor: Prof. Boris Okun \nCommittee Members:\nProfs. Boris Okun\, Craig Guilbault\, Jeb Willenbring\, Jonah Gaster\, and Chris Hruska URL:/math/event/phd-dissertation-defense-mr-william-braubach/ LOCATION:EMS Building\, Room E425\, E425; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E425 E425; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E425; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240426T123000 DTEND;TZID=America/Chicago:20240426T133000 DTSTAMP:20260423T063830 CREATED:20240422T160442Z LAST-MODIFIED:20240422T160442Z UID:10016159-1714134600-1714138200@uwm.edu SUMMARY:Graduate Student Colloquium: Alex Moon DESCRIPTION:Counting Orbits of Defective Parking Functions\nAlex Moon\nPhD Student\nUniversity of Wisconsin-Milwaukee \nParking functions are well-studied objects in combinatorics and representation theory which constitute tuples of preferred parking spots for cars under a linear parking scheme. This talk will generalize to defective parking functions. I will enumerate the orbits of defective parking functions under the action of the symmetric group by characterizing them as nondecreasing tuples and sketching a bijection to standard nondecreasing parking functions. I will also introduce the concept of the conjugate of a nondecreasing parking function in order to simplify the case where the number of cars and spots differ. \nThis is a joint with Pamela E. Harris\, Aaron Ortiz\, Lauren J. Quesada\, Cynthia Marie Rivera Sánchez\, and Dwight A. Williams II. URL:/math/event/graduate-student-colloquium-alex-moon/ LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E495 E495; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E495; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240426T140000 DTEND;TZID=America/Chicago:20240426T150000 DTSTAMP:20260423T063830 CREATED:20240213T185113Z LAST-MODIFIED:20240213T185113Z UID:10016143-1714140000-1714143600@uwm.edu SUMMARY:Colloquium: Fredric Ancel DESCRIPTION: URL:/math/event/colloquium-fredric-ancel/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240430T130000 DTEND;TZID=America/Chicago:20240430T140000 DTSTAMP:20260423T063830 CREATED:20240425T192637Z LAST-MODIFIED:20240425T192637Z UID:10016162-1714482000-1714485600@uwm.edu SUMMARY:MS Thesis Defense: Ms. Helen Kafka DESCRIPTION:Markov Chain Model of Three-Dimensional Daphnia Magna Movement\nMs. Helen Kafka\nUniversity of Wisconsin-Milwaukee \nDaphnia magna make turns through an antennae-whipping action. This action occurs every few seconds\, hence\, during the intervening time\, the animal either remains in place or continues movement roughly along its current course. We view their movement in three dimensions. We divide the movement in the three dimensions into the movement on a two-dimensional lattice and the movement between the different planes. For the movement on the lattice\, we construct a second-order Markov chain model to make predictions about which region of the lattice the animal moves to based on where it was at the last two time points. The movement between the different planes is simulated by a first-order Markov chain. \nAdvisor: Prof. David  Spade \nCommittee Members:\nProfs. David Spade\, Jeb Willenbring\, and Chudamani Poudyal URL:/math/event/ms-thesis-defense-ms-helen-kafka/ LOCATION:EMS Building\, E408\, 3200 N Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.075931;-87.885538 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building E408 3200 N Cramer St Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=3200 N Cramer St:geo:-87.885538,43.075931 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240502T130000 DTEND;TZID=America/Chicago:20240502T150000 DTSTAMP:20260423T063830 CREATED:20240411T204638Z LAST-MODIFIED:20240429T133426Z UID:10016155-1714654800-1714662000@uwm.edu SUMMARY:PhD Dissertation Defense: Mr. Russell Latterman DESCRIPTION:Bayesian Change Point Detection In Segmented Multi-Group Autoregressive Moving-Average Data For The Study Of COVID-19 In Wisconsin\nMr. Russell Latterman\nUniversity of Wisconsin-Milwaukee \nChangepoint detection involves the discovery of abrupt fluctuations in population dynamics over time. We take a Bayesian approach to estimating points in time at which the parameters of an autoregressive moving average (ARMA) change\, applying a Markov Chain Monte Carlo method. We specifically assume that data may originate from one of two groups. We provide estimates of all multi-group parameters of a model of this form for both simulated and real-world data sets. We include a provision to resolve the problem of confounding ARMA parameter estimates and variance of segment data. We apply our model to identify events that may have contributed to the 2020 and 2021 outbreaks of COVID-19 in Waukesha County\, Wisconsin. \nAdvisor: Prof. David Spade \nCommittee Members:\nProfs. Richard Stockbridge\, Istvan Lauko\, Chao Zhu\, and Vytaras Brazauskas URL:/math/event/phd-dissertation-defense-mr-russell-latterman/ LOCATION:EMS Building\, Room E424A\, E424A; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E424A E424A; 3200 N Cramer St. Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E424A; 3200 N Cramer St.:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240502T160000 DTEND;TZID=America/Chicago:20240502T170000 DTSTAMP:20260423T063830 CREATED:20240425T191913Z LAST-MODIFIED:20240425T192108Z UID:10016160-1714665600-1714669200@uwm.edu SUMMARY:MS Thesis Defense: Mr. Lucas Fellmeth DESCRIPTION:Utilizing ARMA Models for Non-Independent Replications of Point Processes\nMr. Lucas Fellmeth\nUniversity of Wisconsin-Milwaukee \nThe use of a functional principal component analysis (FPCA) approach for estimating intensity functions from prior work allows us to obtain component scores of replicated point processes under the assumption of independent replications. We show these component scores can be modeled using classical autoregressive moving average (ARMA) models\, thus allowing us to also apply the FPCA model to non-independent replications. The Divvy bike-sharing system in the city of Chicago is showcased as an application. \nAdvisor: Prof. Daniel Gervini \nCommittee Members:\nProfs. Daniel Gervini\, David Spade\, and Chudamani Poudyal URL:/math/event/ms-thesis-defense-mr-lucas-fellmeth/ LOCATION:EMS Building\, E408\, 3200 N Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.075931;-87.885538 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building E408 3200 N Cramer St Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=3200 N Cramer St:geo:-87.885538,43.075931 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240503T083000 DTEND;TZID=America/Chicago:20240503T090000 DTSTAMP:20260423T063830 CREATED:20240425T192401Z LAST-MODIFIED:20240425T192401Z UID:10016161-1714725000-1714726800@uwm.edu SUMMARY:MS Thesis Defense: Mr. Sven Bergmann DESCRIPTION:Adding a Third Normal to CLUBB\nMr. Sven Bergmann\nUniversity of Wisconsin-Milwaukee \nThe Cloud Layers Unified By Binormals (CLUBB) model uses the sum of two normal probability density function (pdf) components to represent subgrid variability within a single grid layer of an atmospheric model. This binormal approach\, while computationally efficient\, restricts the model’s ability to capture the full spectrum of potential shapes encountered in real-world atmospheric data. This thesis proposes to introduce a third normal pdf component strategically positioned between the existing two\, significantly enhancing the model’s representational flexibility. This trinormal representation allows for a wider range of grid-layer shapes while permitting analytic solutions for certain higher order moments. The core of this work lies in deriving the necessary mathematical transformations for incorporating the third normal pdf seamlessly into the CLUBB framework. This thesis lists all formulas\, inputs\, and outputs associated with the extended model as well as gives an outline\non how to check those equations. Additionally\, it describes certain asymptotic behavior of the trinormal pdf under various parameter settings. \nAdvisor: Prof. Vince Larson \nCommittee Members:\nProfs. Vince Larson\, Peter Hinow\, and David Spade URL:/math/event/ms-thesis-defense-mr-sven-bergmann/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240503T133000 DTEND;TZID=America/Chicago:20240503T140000 DTSTAMP:20260423T063830 CREATED:20240411T204952Z LAST-MODIFIED:20240429T181640Z UID:10016156-1714743000-1714744800@uwm.edu SUMMARY:PhD Dissertation Defense: Mr. Dan Noelck DESCRIPTION:Contraction Rates For McKean-Vlassov Stochastic Differential Equations\nMr. Dan Noelck\nUniversity of Wisconsin-Milwaukee \nThis work focuses on the contraction rates for McKean-Vlasov stochastic differential equations (SDEs)\, McKean-Vlasov Stochastic differential delay equations (SDDEs)\, and path dependent McKean-Vlasov stochastic differential equations.\nUnder suitable conditions on the coefficients of the SDE\, this dissertation derives explicit quantitative contraction rates for the convergence in Wasserstein distances of McKean-Vlasov SDEs using the coupling method. The contraction results are then used to prove a propagation of chaos uniformly in time\, which\nprovides quantitative bounds on convergence rate of interacting particle systems\, and establishes exponential ergodicity for McKean-Vlasov SDEs. The dissertation further develops suitable conditions on the coefficients of the McKean-Vlasov SDDE to obtain a contraction in Wasserstein distance using the coupling method again. These results are used to establish exponential ergodicity for McKean-Vlasov SDDEs. Last the dissertation obtains suitable conditions on the coefficients of the path dependent McKean-Vlasov SDE for a contraction in Wasserstein distance. \nAdvisor: Prof. Chao Zhu \nCommittee Members:\nProfs. Lijing Sun\, Jeb Willenbring\, Richard Stockbridge\, and Peter Hinow URL:/math/event/phd-dissertation-defense-mr-dan-noelck/ LOCATION:EMS Building\, Room E423\, E423; 3200 N Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.0758771;-87.8858312 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E423 E423; 3200 N Cramer St Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=E423; 3200 N Cramer St:geo:-87.8858312,43.0758771 END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240503T140000 DTEND;TZID=America/Chicago:20240503T153000 DTSTAMP:20260423T063830 CREATED:20240422T130711Z LAST-MODIFIED:20240422T131628Z UID:10016158-1714744800-1714750200@uwm.edu SUMMARY:Colloquium: Prof. Genevieve Walsh DESCRIPTION:Hyperbolic groups\, their boundaries and drilling\nProf. Genevieve Walsh\nProfessor of Mathematics\nTufts University \nWe will define and describe groups with a particular geometry\, hyperbolic groups. We will define the boundary of a hyperbolic group and give many examples. If time permits\, we will define a drilling of a hyperbolic group and explore how this operation changes the boundary. Any new work is joint with Groves\, Haissinsky\, Manning\, Osajda and Sisto. URL:/math/event/colloquium-prof-genevieve-walsh/ LOCATION:EMS Building\, EMS E495\, 3200 Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Colloquia ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: END:VEVENT BEGIN:VEVENT DTSTART;TZID=America/Chicago:20240506T130000 DTEND;TZID=America/Chicago:20240506T140000 DTSTAMP:20260423T063830 CREATED:20240506T153439Z LAST-MODIFIED:20240506T153439Z UID:10016163-1715000400-1715004000@uwm.edu SUMMARY:MS Thesis Defense: Mr. Silas Winnemoeller DESCRIPTION:A Finite Element Block Modified Backward Euler Method For Solving A One-Dimensional Poisson-Nernst-Planck Ion Channel Model\nMr. Silas Winnemoeller\nUniversity of Wisconsin-Milwaukee \nIn this thesis\, a finite element block modified backward Euler method is introduced to solve a one-dimensional Poisson-Nernst-Planck ion channel (1D PNPic) model. This model is defined as a system of time-dependent nonlinear partial differential equations\, called Poisson-Nernst equations and Poisson equation\, describing the transport of charged ionic species across a cell membrane via an ion channel pore. For an electrolyte with n ionic species\, its numerical solution gives a prediction to n ionic concentration functions and an electrostatic potential function. However\, solving the 1DPNPic model numerically is challenging due to the model’s strong nonlinearity and numerical stability issues. To address the numerical stability issues\, the traditional backward Euler implicit time scheme is often selected to solve the 1DPNPic model but it may be too costly to be practical in application since it has to solve a system of n + 1 strongly nonlinear partial differential equations at each time step. Hence\, its modification becomes necessary to reduce its computing cost while retaining its numerical stability properly. In this thesis\, the new method is constructed by semi-discretization and finite element techniques such that its each time iteration only involves calculation within two blocks with each block only containing two linear differential equations. Consequently\, the new method can reduce the\ncomputing cost of the Euler scheme sharply. In this thesis\, the new method is implemented as a software package in Python based on the finite element library from the FEniCS project. Numerical tests are then done for an electrolyte with two ionic species\, demonstrating the convergence and high performance of the new method. \nAdvisor: Prof. Dexuan Xie \nCommittee Members:\nProfs. Lei Wang\, Vincent Larson\, and Dexuan Xie \n  URL:/math/event/ms-thesis-defense-mr-silas-winnemoeller/ LOCATION:EMS Building\, Room E416\, 3200 N Cramer St\, Milwaukee\, WI\, 53211\, United States CATEGORIES:Graduate Student Defenses ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu X-TRIBE-STATUS: GEO:43.075931;-87.885538 X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=EMS Building Room E416 3200 N Cramer St Milwaukee WI 53211 United States;X-APPLE-RADIUS=500;X-TITLE=3200 N Cramer St:geo:-87.885538,43.075931 END:VEVENT END:VCALENDAR