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

- 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.

- 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.

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

- T. Day, R. DeLand, J. Juul, Swati, C. Thomas, B. Thompson, and B. Tobin.
*Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields*(In preparation) - 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 - 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).

- 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
- 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* and Talk 2: - 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 Varities of Torus Knots.* - Spring 2018: Student Research Talks, George Mason University,
*An Introduction to Character Varities.* - Spring 2018: Topology Seminar, George Washington University,
*On SL(2,C) Character Varities.* - Fall 2016: Student Research Talks, George Mason University,
*Decomposition of Complex Hyperbolic Isometries by Involution.*

- 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
- 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
- Fall 2020 - MATH 621: Algebra 1 (Graduate)
- 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
- 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.

- 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

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

- 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**

- 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

- American Mathematical Association(AMS)
- Mathematical Association of America(MAA)
- Society for Industrial and Applied Mathematics(SIAM)
- Association for Women in Mathematics(AWM)

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

- 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