Cigole Thomas

I am currently a Postdoctoral Fellow at Colorado State University with Prof. Rachel Pries.

Education

Ph.D. : George Mason University
Dissertation : Stratification and Arithmetic Dynamics on Character Varieties Advisor: Prof. Sean Lawton

Integrated BS - MS: Indian Institute of Science Education and Research (IISER) Mohali, India
Master's Thesis : Decomposition of Complex Hyperbolic Geometry and Involutions
Advisor: Prof. Krishnendu Gongopadhyay

My broad area of research interest is Algebraic Geometry. Specifically, I work on arithmetic dynamics on character varieties. In particular, I look at the action of outer automorphism groups on finite field points of character varieties and explore properties like transitivity, 'large orbits' and asymptotic transitivity. I am also interested in exploring data learning using varieties.

Contact

E-mail: cigole.thomas@colostate.edu.
Official Website: Cigole Thomas
Mail: Louis R. Weber Building
1874 Campus Delivery
Fort Collins, Colorado 80523-1874
Office: Weber 219.

Research Interests

Algebraic Geometry
Arithmetic Dynamics on Character Varieties
Stratification of Character Varieties and E-polynomials
Data Learning using Algebraic Varieties
Math Education
Complex Hyperbolic Geometry

Preprints and Publications

T. Day, R. DeLand, J. Juul, Swati, C. Thomas, B. Thompson, and B. Tobin. Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields, http://arxiv.org/abs/2409.10467
C. Thomas. Asymptotic Dynamics on Character Varieties over Finite Fields (Submitted)
C. Thomas. Action of free type groups (In preparation)
J. Jauchen, H. Klawa, L. Nguyen, R.G. Rebecca, E. Sander, P. Seshaiyer and C. Thomas. Graduate Learning Assistants in the Mathematical Sciences: A new approach to core graduate classes GLAMS: Graduate Learning Assistants in Mathematical Sciences, PRIMUS, 33:8, 819-840
K.Gongopadhyay and C.Thomas. Decomposition of complex hyperbolic isometries by involutions,
Linear Algebra and its Applications, ISSN: 0024-3795, Vol: 500, Page: 63-76

Conference Papers

RG Rebecca, H. Klawa, C. Thomas, L. Nguyen, J. Jauchen, P. Seshaiyer and E. Sander. ON DEMAND: Graduate Assistants supporting active learning in graduate classrooms. Innovations in Teaching and Learning Conference Proceedings Volume 13, 2 September 2021.
Broeckelman-Post M; Fernandez, L; Polk, T; Hwang, J; Thomas, C; Stewart, B; Tuckerman, S; Hassell-Goodman, S; Taylor, S; Nordin, K; Brophy, N; Hingle, A; Staudt, E RC. WORKSHOP: [For GTAs] Engaging Students and Giving Feedback as a GTA. Innovations in Teaching & Learning Conference Proceedings Vol. 12 (2020).

Selected Presentations and Talks

March 2024 : Number Theory Lab, Dynamical irreducibility of certain families of polynomials Colorado State University
January 2024 : Institute Colloquium, University of Denver
September 2023: Panelist: Association for Women in Mathematics Experience as a Woman in Mathematics and Academia Colorado State University
September 2023: AWM Symposium, Session: Women in Groups, Geometry, and Dynamics Arithmetic Dynamics on Character Varieties
June 2023: Plenary Talk, Workshop and school on Complex Lagrangians, Integrable Systems, and Quantization, University of Oxford
April 2023: Speaker and Panelist: Colorado Conference for Underrepresented Students in Mathematics Dynamics of Group Action on Varieties
November 2022: Workshop in Genetics How to create a website using GitHub Iowa State University
October 2022: University of Colorado at Boulder Counting Points on Character Varieties over Finite Fields
October 2022: FRAGMENT(Front Range Algebra GeoMEtry & Number Theory) Arithmetic Dynamics on Character Varieties Colorado State University
February 2022: IISER Math Alumni Talk (Virtual) Dynamics of Group Action on Character Varieties Indian Institute of Science Education and Research Mohali, India
January 2022: Poster session of AWM Special Session on Women in Geometry Dynamics of the outer automorphism group action on SL_2(F_q)- character variety of Z^r.
October 2022: The 3rd JNU-KAIST Geometry Topology Fair, (Virtual) on Talk 1: An Introduction to Character Varieties

Dynamics of the outer automorphism group action on finite field points of character varieties.

September 2021: On-Demand Video Session, Innovations in Teaching and Learning Conference at GMU on Graduate Assistants Supporting Active Learning in Graduate Classrooms (copresented with Hannah Klawa and Long Nyguen).
December 2020: IIP Talks, George Mason University. Algebraic Varieties and Neural Networks.
November 2020: Binghamton University Graduate Conference in Algebra and Topology, Virtual. Conjugacy classes of polystable unimodular commuting matrices over finite fields.
September 2020: Innovations in Teaching and Learning(ITL) Conference, George Mason University. Panelist for Engaging Students and Giving Feedback as a GTA (Virtual).
July 2020: Geometry Labs United, ICERM Brown. A Glimpse into a MEGL Project (Virtual).
Spring 2020: Topology Seminar, George Washington University, The Character Varieties of Torus Knots.
Spring 2018: Student Research Talks, George Mason University, An Introduction to Character Varieties.
Spring 2018: Topology Seminar, George Washington University, On SL(2,C) Character Varieties.
Fall 2016: Student Research Talks, George Mason University, Decomposition of Complex Hyperbolic Isometries by Involution.

Teaching

Instructor

Colorado State University

Fall 2023 - MATH 360: Mathematics of Information Security
- Math 369: Linear Algebra 1
Spring 2023 - MATH 360: Mathematics of Information Security
- Math 301: Introduction to Combinatorics
Fall 2022 - MATH 360: Mathematics of Information Security

George Mason University

Summer 2022 - MATH 203: Linear Algebra
Summer 2019 - MATH 113: Analytic Geometry and Calculus 1
Summer 2018 - MATH 125: Discrete Mathematics 1
Summer 2017 - MATH 108: Introductory Calculus with Business Applications
Summer 2016 - MATH 108: Introductory Calculus with Business Applications

Graduate Learning Assistant (George Mason University)

Fall 2020 - MATH 621: Algebra 1 (Graduate)

Graduate Teaching Assistant (George Mason University)

Spring 2020 - MATH 114: Analytic Geometry and Calculus 2
Fall 2019 - MATH 114: Analytic Geometry and Calculus 2
Spring 2018 - MATH 113: Analytic Geometry and Calculus 1
Fall 2017 - MATH 114: Analytic Geometry and Calculus 2
Spring 2017 - MATH 114: Analytic Geometry and Calculus 2
Fall 2016 - MATH 114: Analytic Geometry and Calculus 2
Spring 2016 - MATH 114: Analytic Geometry and Calculus 2

NSF - Improving Undergraudate STEM Education(IUSE) project at GMU

Developed Inquiry Based Learning (IBL) worksheets to promote group work and discussion among students for Calculus 1 and Calculus 2.
Co-organized biweekly Teaching Seminar to discuss the challenges and progress of the implementation of IBL worksheets in calculus recitations.
Coordinated other teaching assistants involved in IUSE project.

Committee Member

Spring 2022 : Hiring Committee Member for Mason Experimental Geometry Lab Outreach Director

Spring 2021, Spring 2022 : Graduate student representative in the GMU College of Science Diveristy, Equity and Inclusion subcommittee for Graduate Student Recruitment, Retention, and Degree Attainment

Leadership

Mason Experimental Geometry Lab(MEGL)

Spring 2019 - Spring 2020 : Graduate Lab Assistant
Spring 2016 - Fall 2018 : Graduate Student Mentor for research team of undergraduate students.
Spring 2016 - Fall 2018 : Graduate Student Intern
Summer 2015 : Graduate Student Intern
Volunteer for MEGL outreach events

Association for Women in Mathematics (AWM) - GMU Chapter

March 2020 - March 2022 : Vice President
March 2018 - March 2020 : President
March 2017 - March 2018 : Treasurer
March 2016 - March 2017 : Vice President

Seminars and Conference Organization

Number Theory Lab at Colorado State University Fall 2022, Spring 2023, Fall 2023 Co-organizer
Postdoc Seminar at Colorado State University Fall 2022, Spring 2023, Fall 2023 Co-organizer
AMS Contributed Paper Session on Algebraic and Arithmetic Geometry and Commutative Algebra JMM 2022, Chair (Virtual)
Student Research Talks (StReeTs) at GMU Orgnaizer/Co-organizer Fall 2018 - Spring 2020
AWM/IIP Talk at GMU by Anne Costolanski (Georgia Tech) on Navigating a technical career as a woman in STEM, Coorganizer Nov 2021
AWM Young Mathematician Talk at GMU - April 2021 (Virtual), Organizer
ECOM 2019 : Volunteer and secured partial funding as President of AWM
Professional Development Event for Aspiring Mathematicians: Coorganizer
MRC: Character Varieties and its Frontiers in June 2016: Assistant to Organizers

Mathematics Outreach

Spring 2021 (Virtual): Panel member of Outreach Session for girl students in Nepal , 'Math Initiatives in Nepal' as part of Kovalesky Day
Spring 2020 (Virtual) and Spring 2021 (Virtual): Co-organizer, Outreach event for Women in Math Society (WIMS) Members of Centreville High School
Spring 2017, Spring 2018, Spring 2019 - Coorganizer, AWM WIMS Centreville High School Girls Visit at GMU
Spring 2016, Spring 2018: Volunteer at SIAM Booth, USA Science and Engineering Festival
Spring 2017: AWM Volunteer, National Math Festival
Spring 2016 - Fall 2019 : Volunteer, MEGL outreach events
Feb 2017, Feb 2018 and Feb 2019: Grader, MATHCOUNTS

If you are interested in or need more information about any of the activities listed here, feel free to email me at Cigole.Thomas@colostate.edu.

Curriculum Vitae

Click here.

Some useful links.

National Mathematical Organizations

Opportunities

MathPrograms : To search and apply for internships
MathJobs: To search and apply for jobs in mathematics(postdocs, teaching positions etc.)

Some Interesting Articles

AMS Early Career Collection: An amazing collection of monthly thematic compilations of articles aimed at early career academics of all types.
Mathematicians Set Numbers in Motion to Unlock Their Secrets, Quanta Magazine : A nice article on arithmetic dynamics