contents - Chris Jankowski, Lecture notes of Algebra

Download contents - Chris Jankowski and more Lecture notes Algebra in PDF only on Docsity! CHRISTOPHER JANKOWSKI SENIOR ACADEMIC PROFESSIONAL SCHOOL OF MATHEMATICS GEORGIA INSTITUTE OF TECHNOLOGY NOVEMBER 3, 2021 CONTENTS I. Earned Degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 II. Employment History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 III. Honors and awards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 IV. Summary of Higher Education Administrative and Leadership Experience . . . . . . . . . . . . . . . . . . . . . . . 2 V. Education and Mentorship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 A. Courses Taught . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 B. Academic and Career Advising and Guidance Responsibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 C. Educational Innovations and Other Contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 VI. Research, Scholarship, and Creative Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 A. Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 B. Other Publications and Creative Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 C. Presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 VII. Service. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 A. Public and Community Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 B. Institute Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 C. Other Professional Activities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 VIII.Professional Growth and Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 1 2 CHRISTOPHER JANKOWSKI CHRISTOPHER JANKOWSKI SENIOR ACADEMIC PROFESSIONAL SCHOOL OF MATHEMATICS I. EARNED DEGREES 2009 Ph.D. in Mathematics, University of Pennsylvania. Dissertation: On type II0 E0-semigroups induced by q-pure maps on Mn(C). Thesis Advisor: Robert T. Powers. 2004 B.S. in Mathematics, University of Notre Dame, summa cum laude. II. EMPLOYMENT HISTORY 2016–present Academic Professional, Georgia Institute of Technology. 2012–2016 Clinical Assistant Professor, New York University. 2011–2012 Lecturer, University of Pennsylania. 2009–2011 Postdoctoral Fellow, Ben-Gurion University of the Negev, Israel. Supervisor: Daniel Markiewicz. III. HONORS AND AWARDS 2020 Eric R. Immel Memorial Award for Excellence in Teaching, Georgia Institute of Tech- nology. 2016-present Recipient of ten Thank a Teacher certificates, Georgia Institute of Technology. 2007 Moez Alimohamed Graduate Student Teaching Award, Department of Mathematics, University of Pennsylvania. Awarded to one graduate student in the math department each year. IV. SUMMARY OF HIGHER EDUCATION ADMINISTRATIVE AND LEADERSHIP EXPERIENCE Georgia Institute of Technology, 2016-2020 2017–present Director of Graduate Advising and Assessment, School of Math. The position encompasses a broad range of administrative duties for the graduate pro- gram. These include serving on the Graduate Committee, writing annual student evalu- ations and handling comprehensive exams, ensuring Responsible Conduct in Research compliance from first-year doctoral students, organizing meetings for Admitted Stu- dents Day, filing annual OATS reports for the MS Math and PhD Math programs, and handling transfer credit requests for graduate-level mathematics courses. 2017–present Director of Postdoctoral Teaching Effectiveness, School of Math. I mentor postdoctoral faculty in teaching during their first year, and I participate in organizing and running professional development events for the postdoctoral faculty. In addition, I follow their teaching performance throughout their time at Georgia Tech, communicate with their mentors and the Postdoc Committee when appropriate, and assist the Postdoc Committee in writing its annual evaluation letters. Fall 2017–Spring 2020 and Spring 2021 Course Coordinator, Math 1553 (Introduction to Linear Algebra). From Fall 2017 through Spring 2020, Math 1553 was the Institute’s largest math course CURRICULUM VITAE 5 FASET orientations over the summer, then handled on-campus undergraduate ad- vising for a period when the DUAA was teaching abroad during Fall 2017. New York University, 2012-2016 2012-2016 Math Major Advisor. A portion of the math majors looking for guidance regarding their coursework trajectory could seek my advice. C. EDUCATIONAL INNOVATIONS AND OTHER CONTRIBUTIONS 2020 Co-author, PEGS Proposal for School of Math: Recruitment. Co-authors were Mitchell Everett and Xingxing Yu. The proposal was awarded $20, 000 by the Georgia Institute of Technology. 2017 Contributor to Course Coordination Proposal, Georgia Institute of Technology. Along with a group of several faculty members, I contributed to the writing of the course coordination proposal. It passed through a faculty vote, and it has been School of Math policy for some of our core mathematics courses since Fall 2017. 2014–2015 Calculus I hybrid course, New York University. Dr. Selin Kalaycioglu, Dr. Drew Youngren, and I created an interactive Calculus I course with the help of an NYU video team. Outside of lecture, students watch videos and participate in assessments we created. They access course readings online and view other material at their class’s website. The class launched in Fall 2015. 2012 Math for Economics III Curriculum, New York University. Collaborated with Dr. Selin Kalaycioglu to write the syllabus for the course. VI. RESEARCH, SCHOLARSHIP, AND CREATIVE ACTIVITIES A. PUBLICATIONS All publications below are in refereed journals. *Indicates publications at Georgia Tech. (1) *Classification of q-pure q-weight maps over finite dimensional Hilbert spaces, with Daniel Markiewicz and Robert T. Powers, J. Funct. Anal. 277 (2019), no. 6, 1763-1867. (2) Aligned CP-semigroups, with Daniel Markiewicz and Robert T. Powers, Int. Math. Res. Not. IMRN 2015, no. 15, 6639-6647. (3) Unital q-positive maps on M2(C) and cocycle conjugacy of E0-semigroups, Houston J. Math. 39 (2013), 1233-1266. (4) A family of non-cocycle conjugate E0-semigroups obtained from boundary weight doubles, J. Operator Theory 69 (2013), no. 1, 233-256. (5) E0-semigroups and q-purity: boundary weight maps of range rank one and two, with Daniel Markiewicz and Robert T. Powers, J. Funct. Anal. 262 (2012), no. 7, 3006-3061. (6) Gauge groups of E0-semigroups obtained from Powers weights, with Daniel Markiewicz, Int. Math. Res. Not. IMRN 2012, no. 14, 3278-3310. 6 CHRISTOPHER JANKOWSKI (7) On type II0 E0-semigroups induced by boundary weight doubles, J. Funct. Anal. 258 (2010), no. 10, 3413-3451. (8) On K∗-ultrahomogeneous graphs, with Daniel Isaksen and Stephanie Proctor, Ars Combin. 82 (2007), 83-96. B. OTHER PUBLICATIONS AND CREATIVE PRODUCTS Problem sets for Interactive Linear Algebra, by Margalit and Rabinoff. Outside my job of course coordination, I have compiled a collection of homework problems. This is still in progress, and the goal is to incorporate these into the textbook in the future. C. PRESENTATIONS C1. Invited Talks Spring 2017 Prime E0-semigroups. Mathematics Colloquium, Georgia Southern Uni- versity. Spring 2015 The Evolving Classroom. Special Colloquium, University of California- Irvine. Spring 2015 Mathematics in Cryptography. Undergraduate Colloquium, University of California-Irvine. Spring 2015 Addressing Students’ Needs in a Changing Classroom. Rice University. Spring 2012 To infinity and beyond: what they didn’t teach us in linear algebra. Colloquium, Manhattan College. Spring 2011 The realm of positivity in linear algebra. Bryn Mawr College, Spring 2011. Spring 2011 Completely positive maps and noncommutative dynamics. Analysis Sem- inar, Drexel University. Fall 2010 E0-semigroups and boundary weight doubles. Math Department Collo- quium, United States Naval Academy. C2. Selected other talks Summer 2014 Prime E0-semigroups. Great Plains Operator Theory Symposium, Kansas State University. Summer 2013 Boundary weight maps and E0-semigroups. Great Plains Operator The- ory Symposium, University of California-Berkeley. Spring 2011 Gauge groups of E0-semigroups. Function Theory and Operator Theory: Infinite Dimensional and Free Settings, Ben-Gurion University of the Negev. Fall 2009 Local cocycles of certain E0-semigroups of type II0 after Alevras, Pow- ers, and Price (parts 1 and 2). Operator Algebras Seminar, Ben-Gurion University of the Negev. Summer 2009 E0-semigroups induced by q-pure maps on Mn(C). Great Plains Operator Theory Symposium, University of Cincinnati. CURRICULUM VITAE 7 VII. SERVICE A. PUBLIC AND COMMUNITY SERVICE 2013-2014 Research Mentor, NYU GSTEM Program. I volunteered to mentor two high school students in a program for young women in math, covering some basics of number theory and guiding each student through a summer project. The students and their research projects are listed below. (1) Summer 2014: Alisa Chang, RSA cryptography from scratch and improving it through the use of cyphers. (2) Summer 2013: Eshka Ne-Kumar, The nature of odd primes and perfect squares in the triangular numbers. B. INSTITUTE CONTRIBUTIONS 2020 Lead organizer of Mandatory Title IX Session for doctoral students in the School of Math. The session was conducted by Marcia Bull Stadeker, Georgia Tech’s Title IX Co- ordinator in the Office of Ethics, Compliance, and Legal Affairs. 2020–present Institute Assessment Council member. 2017–2019 Lead Organizer (2017 and 2018) and Co-Lead Organizer (2019) of the Geor- gia Tech High School Math Competition (2017 and 2018), School of Math. The competition is the Georgia Tech School of Math’s largest community out- reach event. It hosts 200-300 students from the Atlanta for a full-day event each Spring. The top finishers receive fellowships if admitted to Georgia Tech. 2017–present Graduate Committee member, School of Math. Secretary of the committee during the 2018–2019 academic year. 2017–present Teaching Panels for Tenure-Track Candidates, School of Math. Served on approximately 20 interview panels for asking and addressing ques- tions related to teaching and the graduate program. 2017–present Contributor, School of Math Course Materials Respository. The repository hosts many resources for faculty teaching six of our core courses. I have posted materials there for Math 1553 and Math 2551. 2020 Judge, The Career, Research, and Innovation Development Conference (CRIDC) Poster Session, Georgia Institute of Technology. 2018 School of Math Liaison, Insight Data Science Workshop and Tech Session, School of Math. 2016 Judge, Research Bound Poster Session, College of Sciences. C. OTHER PROFESSIONAL ACTIVITIES 2020 T-Book Interview for the 2020 Georgia Tech T-Book. T-Books are annually dis- tributed to incoming undergraduate students. 2015 Committee Member for Ph.D. Candidacy Exam, Leonard Stevenson, Drexel University.