Project: Morse Flow Trees

Total Page：16

File Type：pdf, Size：1020Kb

Project: Morse Flow Trees Kenneth Blakey | Sangjun Ko Brown University | Rutgers University June 1, 2021 Prepared While Participating at DIMACS REU 2021 Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 1/9 Outline 1 Morse Theory 2 Symplectic Topology 3 Projects Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 2/9 Morse Theory Morse theory studies the topology of a smooth manifold via smooth functions on that manifold. n b Cold h Con Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 3/9 Morse Homology Morse theory comes equipped with a homology theory that looks at flow lines connecting critical points. Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 4/9 Symplectic Topology Symplectic topology studies smooth manifolds equipped with a symplectic form. Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 5/9 Lagrangian Submanifolds Lagrangian submanifolds are maximal submanifolds such that the symplectic form vanishes identically. Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 6/9 Flow Trees Flow trees are tree-like objects where each branch consists of flow lines. Project: For what general defining data is the space of Morse flow trees compact Hausdorff? Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 7/9 Lagrangian Floer Homology and Fukaya Categories Lagrangian Floer homology is an intersection theory for Lagrangian submanifolds that is unchanged by symplectic deformations. Using these ideas one can define the Fukaya Category. connecting points stripintersection Lagrangian's E intersection pants Project: Producing isotopies for pairs of Lagrangians through categorical techniques. Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 8/9 Acknowledgements 1 We’d like to thank our mentor Christopher Woodward and his graduate students Soham Chanda and Cindy Zhang for working with us this summer. 2 Work supported by the Rutgers Department of Mathematics, NSF grant DMS-1711070, and the DIMACS REU program. Kenneth Blakey | Sangjun Ko (Brown UniversityProject: | Rutgers Morse University) Flow Trees June 1, 2021 9/9.

Copy Link

Recommended publications

Rutgers University Step-By-Step Guide New Organization Recognition for Undergraduate Student Organizations Starting a New Organi
Rutgers University Step-by-Step Guide New Organization Recognition for Undergraduate Student Organizations Starting a New Organization at Rutgers University – New Brunswick Student organizations provide an outlet to connect and develop with others, create and express ideas, and inspire and impact the community. This resource packet provides valuable tips for establishing a new organization on campus. It also provides policies and guidelines that must be adhered to in order to be recognized and registered by Rutgers University. Questions? Contact the Department of Student Centers & Involvement at [email protected]. We encourage you to attend a one-on-one informational workshop with our peer advisors to expedite your recognition process. Email the department your availability to schedule your workshop. PART 1: Create a Profile Step 1: Draft a Statement of Purpose for your organization’s Constitution First, develop a Statement of Purpose that will serve as the underlying foundation for your group. Consider the following: What do we hope to accomplish? How will we serve Rutgers University and its students? How are we distinctly different from other organizations? What do we value, hope for, believe in, and support? Are we part of a larger organization or cause? In your statement of purpose, you must also describe 2-3 events or programs that the organization intends to host. Step 2: Develop the Constitution The Constitution provides the operating framework of the group. We recommend that you use the “Sample Constitution” as a guide (See guide below). The following articles must be included in your organization’s constitution: * Name and acronym/short phrase of your organization * Statement of purpose * Active membership/ voting privileges * Title and role description for all officers * Officer election, selection, and removal method Must be an entirely democratic process (i.e.
[Show full text]
Class of 2015: Future Plans (Alphabetical)
Class of 2015: Future Plans (alphabetical) Click the image to view the full page, or browse the list below: Crystal Abbott Mercer County Community College Elias Abilheira Cornell University Lila Abreu Princeton University Alix Adam Rutgers University Odin Adams-Tuck Embry-Riddle Aeronautical University Leah Adams Mercer County Community College Patricia Aguiar Princeton University Alisa Ali The College of New Jersey Mohammad Alkhafaji Rutgers University Ian Alloway Rutgers University Alejandro Altamirano Monmouth University Judy Anderson Other plans Jackson Andres Drexel University Evelin Aparicio Mercer County Community College Hannah Ash Occidental College Amnon Attali Rutgers University Honors College Noa Attali Rutgers University Honors College Andrew Bai University of California, Berkeley Jessica Bai Columbia University Ananth Balasubramanian University of Chicago Larry Bao Princeton University Andrew Barry Stevens Institute of Technology Hayley Bell Gettysburg College Victor Bell Rowan University Eszter Bentch Wheaton College Morgan Bestwick University of Arizona Rhea Bhatt University of South Florida Lydia Bhattacharya McGill University Helen Bichsel School of the Art Institute of Chicago Iona Binnie Williams College Francisco Bischoﬀ Could not be reached Class of 2015: Future Plans (alphabetical) Aidan Bitterman Pennsylvania State University Karl Bjorkman St.Olaf College Briana Blue Rider University Julie Bond University of Virginia Barnabe Bouchenoir Declined to respond Kyle Brady Cooper Union Rhea Braun Princeton University
[Show full text]
Class of 2011
EDUCATION INTERnatIONAL STUDIES NEUROSCIENCE Chicago School of Professional New York University-Occupational Employment John Read Middle Sch. (CT) Employment Graduate/Professional School Employment Marywood University-Physician’s Psychology-Child/Adolescent Therapy Capital Sch. Dist. (DE) Lehighton H.S. (PA) Accenture Drexel University College of Medicine- CRI Lifetree Assistant Psychology New York University-Psychology Cardin School (MD) North Star Academy (NJ) Command Security Corp. Medicine Kessler Foundation Philadelphia College of Osteopathic Columbia University-Counseling New York University-Social Work (2) DePaul Catholic H.S. (NJ) St. Helena’s School (PA) EastWest Institute New York University-Nursing St. Barnabas Medical Center Medicine-Biomedical Sciences Psychology Queens College-Art History Dulce Independent Sch. Dist. (NM) Teach For America (LA) Kimball Medical Center Rutgers University-City/Regional Teach for America St. George’s University Medical School Columbia University-Education Administration Fairfax Co. Public Schools (VA) Teach For America (NC) Planning Thomas Jefferson University Hospital (Greneda)-Medicine Columbia University-Psychology Rowan University-School Counseling Fair Lawn Sch. Dist. (NJ) (3) The School for Excellence (NY) Seton Hall University-Diplomacy/ Toms River Reg. Sch. Dist. Thomas Jefferson University- Fordham University-School Counseling Seton Hall University School of Law- Foote School (CT) Tian Chi Language Learning Ctr. (China) International Relations Physical Therapy Georgian Court University-Psychology
[Show full text]
Request for Application New Jersey Alliance for Clinical and Translational Science (NJ ACTS)
Request for Application New Jersey Alliance for Clinical and Translational Science (NJ ACTS) Partnership & Innovation Pilot Grant Program Funding Opportunity Purpose: The purpose of this RFA is to solicit applications for partnership and innovation pilot grants from investigators at Rutgers University, Princeton University and New Jersey Institute of Technology. Release Date: July 29th, 2019 Letter of Intent: Monday, August 12th, 2019 (Strongly encouraged, not required) Application Deadline: Tuesday, September 3rd, 2019 Award Notification: October 2019 dependent on NCATS approval Earliest Start Date: October 2019 dependent on NCATS approval NJ ACTS, an NIH Clinical and Translational Science Awards Program (CTSA) partnership between Rutgers, Princeton University and New Jersey Institute of Technology (NJIT), is pleased to announce a community partnership and innovation funding program. Objective The purpose of the Partnership and Innovation Accelerator Pilot Grant Program (PIAP) is to facilitate collaborations between academic researchers from Rutgers University, Princeton University, and New Jersey Institute of Technology and community organizations so they can work together on health research that benefits the community. The researcher/community partnerships facilitated by this mechanism will seed and/or strengthen new or existing partnership projects. These awards, up to $10,000 for 1 year, support areas of mutual interest, define the relationships and expectations of the partnership, create a structure for the partnership, and define
[Show full text]
1 COVID-19 Whole Family Approach Impact Research September 2020
COVID-19 Whole Family Approach Impact Research September 2020 Dr. Amy Castro Baker and team at the University of Pennsylvania are currently in the midst of an outcome and process evaluation of two social service collaboratives in the New York City metro area: Familia Adelante in the South Bronx, serving the Mott Haven, Concourse Village, and Melrose neighborhoods, and Families for Literacy in Jersey City, NJ, serving the Communipaw, McGinley Square, and Journal Square areas. Both of these collaboratives are instances of the Pascale Sykes Foundation’s Whole Family Approach, a social service provision and funding model that posits that social and economic resilience among working poor families can be effectively cultivated when organizations collaborate to deliver social services to the entire household. These interventions seek to interrupt cycles of intergenerational poverty through support services that address financial stability and mobility, child and adult wellbeing, and healthy family relationships. Since December 2017, the research team at the University of Pennsylvania has been gathering data about the impact of this approach using a mixed methods research design that combines quantitative outcome measurements (survey data; clinical data-mining) with qualitative data collection (clinical data mining; semi-structured interviews; participant observation). This design maximizes our ability to understand both what is happening inside the interventions as well as why these changes are occurring. In early 2020, the emergence of Covid-19 drastically and fundamentally changed the organization of social and economic life in the United States. Many workplaces shuttered their doors, as white-collar workers shifted to home-based work, while many blue-collar workers, unable to earn their living remotely, faced job loss or reductions in pay.
[Show full text]
Returning to Rutgers University – Newark: a Working Plan for Fall 2020
Returning to Rutgers University – Newark: A Working Plan for Fall 2020 Revised August 13, 2020 CONTENTS INTRODUCTION .......................................................................................................................... 3 ACADEMIC PLAN ........................................................................................................................ 4 Courses Usually Held on Campus .............................................................................................. 4 Technology Support for Faculty and Students............................................................................ 5 STUDENT ACADEMIC SUPPORT ............................................................................................. 8 Tutoring....................................................................................................................................... 8 Advising ...................................................................................................................................... 8 RESEARCH .................................................................................................................................. 10 STUDENT AFFAIRS ................................................................................................................... 11 Athletics and Recreation ........................................................................................................... 11 Career Development ................................................................................................................
[Show full text]
Rutgers University-Newark Resources-SOAR
Rutgers University-Newark Resources-SOAR IN NEWARK, OF NEWARK myRUN myRUN.newark.rutgers.edu Easy to access, mobile friendly Provides access to relevant information in one location 973-353-1766 Ext. 1 if you should have any questions Will deploy a chat feature in the coming months IN NEWARK, OF NEWARK IN NEWARK, OF NEWARK myRutgers portal Mobile Device friendly 5 Scarlet Email • University sends emails to official university emails • Students are responsible for checking email • Step by Step instructions for setting up your Scarletmail • Scarletmail FAQs • Set up via phone • Forward to another address • For more information go to myRUN > My Grades & Records > Personal Information IN NEWARK, OF NEWARK NetID • The university uses NetID as a sign-on identifier instead of the student ID number • In order to access many of the electronic services available to you at Rutgers, you need to activate your Rutgers NetID. • Set up via https://netid.rutgers.edu/index.htm • For more about personal information go to My Grades & Records > Personal Information via MyRUN website IN NEWARK, OF NEWARK Family Educational Rights and Privacy Act (FERPA) • Federal law 1974 • You have to provide permission to the university about who will have access to your educational records • Overview can be found on myRUN at https://myrun.newark.rutgers.edu/privacy-students • Must complete form and bring to Office of the Registrar IN NEWARK, OF NEWARK HEALTH INSURANCE All undergraduate and graduate full-time students are required to have comprehensive health insurance every semester. If you have other comparable health insurance coverage, you must waive the insurance and get the premium removed from your term bill.
[Show full text]
1 CURRICULUM VITAE Leslie Mccall Department of Sociology 1810 Chicago Avenue Northwestern University Evanston, IL 60208-1330
CURRICULUM VITAE Leslie McCall Department of Sociology 1810 Chicago Avenue Northwestern University Evanston, IL 60208-1330 [email protected] http://www.ipr.northwestern.edu/faculty-experts/fellows/mccall.html EDUCATION 1995 Ph.D., University of Wisconsin, Madison, Department of Sociology 1990 M.A., University of Wisconsin, Madison, Department of Sociology 1986 B.A., Brown University, Departments of Computer Science and Third World Development Studies POSITIONS HELD 2013- Professor, Northwestern University 2012- Courtesy Appointment, Department of Political Science 2010-2014 Director of Undergraduate Studies, Department of Sociology 2006- Faculty Fellow, Institute for Policy Research 2006-2013 Associate Professor, Northwestern University, Department of Sociology 2001-2006 Associate Professor, Rutgers University 1995-2001 Assistant Professor, Rutgers University Department of Sociology (75%)/Women’s Studies Program (25%) AREAS OF SPECIALIZATION Social Inequality and Demography: Gender, Class, and Race; Political Sociology; Economic Sociology; Social Theory; Methodology AWARDS, HONORS, AND MEMBERSHIPS 2012-2013 Public Voices Fellowship, Northwestern University 2012 Visiting Scholar, Institut d’Etudes Politiques de Paris (Sciences Po) 2011- Elected Member, Sociological Research Association 2010-2013 Board Member, General Social Survey 2009 Best Article Award, 2008, Socio-Economic Review 2008-2009 Visiting Scholar, Center for the Study of Democratic Politics, Princeton University 2008-2013 Editorial Boards, Sociological Theory, Socio-Economic Review, Social Politics 2006- Fellow, Center for the Study of Poverty & Inequality, Stanford University 2005-2007 Member, National Science Foundation Sociology Advisory Panel 2003-2004 Faculty Fellow, Rutgers Center for the Critical Analysis of Contemporary Culture 2003-2005 Editorial Board, American Sociological Review 2002-2003 Senior Fellow, Demos: A Network of Ideas and Action 2002 First Runner-up, C.
[Show full text]
Scarlet Knight Invitational
Scarlet Knight Mock Trial Invitational Hosted by the Rutgers University Mock Trial Association Tabulation Summary Team Round 1 Round 2 Round 3 Round 4 Summary Δ v. Fordham Π v. Amherst B Δ v. Haverford B Π v. NYU A 4-3-1 American University L W W W T W L L CS PD OCS -10 7 18 20 0 5 -6 -14 19 20 63.5 Δ v. Haverford A Π v. Monmouth A Π v. Quinnipiac Δ v. Pitt B 2-6-0 Amherst College A L L W W L L L L CS PD OCS -5 -8 8 3 -10 -15 -5 -5 10.5 -37 59 Π v. Haverford B Δ v. American Δ v. Pace Π v. Monmouth B 1-7-0 Amherst College B L L L L L L W L CS PD OCS -5 -34 -18 -20 -16 -5 6 -12 15.5 -104 56.5 Δ v. Penn State B Π v. Penn State A Π v. Pitt B Δ v. Monmouth A 3-5-0 Dickinson College L L L L W L W W CS PD OCS -13 -1 -12 -13 4 -5 9 16 14 -15 53 Π v. American Δ v. Haverford B Π v. Monmouth A Δ v. Princeton B 5-2-1 Fordham University-Rose Hill W L W L W W T W CS PD OCS 10 -7 10 -27 16 5 0 13 13.5 20 58.5 Π v. Amherst A Δ v. NYU A Δ v. UMD B Π v.
[Show full text]
Press Release
Theatre Arts and Performance Studies Box 1897 83 Waterman Street Providence, RI 02912 401-863-3283 Fax 401-863-7529 PRESS RELEASE FOR IMMEDIATE RELEASE Department of Theatre Arts and Performance Studies, Brown University 83 Waterman Street, Providence, RI 02912 Contact: PauL Margrave, Marketing Coordinator (401) 863-2730 / [email protected] / brown.edu/theatre Tuesday, September 20, 2016 BROWN UNIVERSITY AND THE DANIEL JORDAN FIDDLE FOUNDATION FOR ADULT AUTISM ANNOUNCE NEW ENDOWMENT FUND FOR THE ARTS Foundation Gift Supports Theater Programs to Benefit Autistic Adults Providence, RI — Brown University Department of Theatre Arts and Performance Studies announced today that The DanieL Jordan FiddLe Foundation (DJFF), the nation's first not-for-profit organization to exclusiveLy focus on aduLt autism, wiLL estabLish a new endowment fund at Brown University. This fund wiLL add to DJFF's existing endowed program initiatives at Rutgers University, YaLe University, and the University of Miami. With a gift of $100,000, The DanieL Jordan FiddLe Foundation AduLt Autism Theater and Performing Arts Fund at Brown University wiLL be estabLished. The fund wiLL support programs, education, and performance experiences in the Brown University Department of Theatre Arts and Performance Studies (TAPS). The activities wiLL benefit young aduLts and aduLts diagnosed with Autism Spectrum Disorder (ASD). It wiLL aLso provide experientiaL and educationaL opportunities for undergraduate and graduate students to work directLy with the aduLt autism popuLation. The DJFF Fund wiLL enabLe Brown University students and participants from the Artists and Scientists as Partners program in Rhode Island to Learn the methodoLogy of master teacher Elaine HaLL, Founder of The Miracle Project.
[Show full text]
Editorial Style Guide
RUTGERS UNIVERSITY–CAMDEN Editorial Style Guide Revised July 2016 This editorial style guide has been developed as a quick reference tool for anyone writing about Rutgers University‒Camden. It provides basic guidelines for frequently raised questions of style, as well as specific standards of usage for Rutgers‒Camden. Using a style guide helps to eliminate inconsistencies in spelling, grammar, and punctuation and to promote clear, professional writing. Contents University names 4 Logos and visual identity 5, 6 Building and location names 7 Venues / Sculpture and landmarks on campus 8 Alumni designations 9 School and college initials 10 Abbreviations / Academic degrees 11 Addresses / Adviser / Athletics 12 Beside, besides / Bullets 13 Capitalization / Comma 14 Dates / Ellipsis / Em dash, en dash 15 Email signature and return address 16 Gender-specific language / Hyphen 17 Italics / More important / Numbers 18 Plural and possessive 19 Prefixes 20 Religious references 21 States, cities, countries, state abbreviations / Suffixes 22, 23 That or which / Time 24 Titles / Unit names / Web address 25 UNIVERSITY NAMES • Rutgers University–Camden (primary reference) • Rutgers–Camden (secondary reference) • School of Business–Camden (external reference: Rutgers School of Business–Camden) • Rutgers Law School (not Rutgers Law School–Camden) • School of Nursing–Camden (external reference: Rutgers School of Nursing–Camden) • Faculty of Arts and Sciences–Camden (external reference: Rutgers–Camden Faculty of Arts and Sciences) • Camden College of Arts and Sciences (external reference: Rutgers–Camden College of Arts and Sciences) • University College–Camden (external reference: Rutgers–Camden University College) • Graduate School–Camden (external reference: The Graduate School at Rutgers–Camden) Rutgers University–Camden is the primary reference for the institution and must appear at least once in a communication about the institution.
[Show full text]
Scarlet Knight Battalion
SCARLET KNIGHT BATTALION VOLUME 1, ISSUE 1 OCTOBER 2017 FROM THE CADET BATTALION COMMANDER By C/LTC Stephen Morancie ter I’ve spent at Rutgers. tunity make some of your This year marks the start of For me, college and ROTC closest friends, who you’ll INSIDE THIS ISSUE: a concerted effort to safe- are inexorably linked. It was have the privilege of serving the Scarlet Knight battalion with after graduation. guard the institutional BASIC AND 2 that gave me the opportuni- ADVANCED CAMP knowledge each class devel- I say “can” because none of ty to go to college in the ops during its time in the these things are a given. The CADET SUMMERS 2 first place. When you enter battalion. Juniors are not program requires a lot more college as a SKBN cadet, just rotating through com- grit than anything else on you don’t come in blind like RANGER CHALLENGE 3 pany leadership positions; campus. Army Officers are everyone else. You become they are now being attached expected to be self motivat- part of an organization of GERMAN ARMED FORCES 3 to the battalion staff to ing and disciplined; you will PROFICIENCY BADGE leaders and mentors com- jumpstart their learning as be held to the same stand- mitted to your growth and DAY IN THE LIFE 3 future MS4’s. Continuity ards. However, if you have OF A NEW CADET professional development. books have been created for the drive the dedicated This program can teach you CALENDAR OF 4 every position to help fu- team of cadre and seniors everything from discipline, EVENTS ture classes build upon the will give you the education tactics, time management; lessons of those before you need to achieve your and above all, leadership.
[Show full text]