Presentations

Invited Talks

1. Factorizations of groups and skew braces (slides)

   • Ischia Group Theory

   • Grand Hotel delle Terme Re Ferdinando at Ischia, Italy (April 8 – April 12, 2024)

2. On the relationship between the additive and multiplicative groups of a skew brace (notes)

   • Research on Finite Groups, Algebraic Combinatorics, and Vertex Algebras

   • Research Institute for Mathematical Sciences Kyoto University, Japan (Dec 18 – Dec 21, 2023)

3. The multiple holomorph of centerless groups (slides)

   • Ischia Online Group Theory Conference (weekly e-seminar)

   • Online (July 15, 2021)

4. Hopf-Galois structures: a brief introduction and their associated isomorphism type (slides)

   • Seventh NZ Number Theory Workshop

   • Online & University of Waikato, New Zealand (Nov 9, 2020)

5. An introduction to the group-theoretic aspects in Hopf-Galois theory (slides)

   • Summer Program on Number Theory and Related Topics: Program on Galois Structures in Number Theory

   • Harbin Institute of Technology, China (Aug 12 – Aug 13, 2019)

6. Normal integral basis and realizable classes (slides)

   • Women and Mathematics: Aspects of Algebraic Geometry

   • Institute for Advanced Study, Princeton, USA (May 11 – May 22, 2015)

Presentations at Selected Conferences

1. Maschke's theorem and irreducible representations for skew braces (upcoming)

   • Hopf Algebras & Galois Module Theory

   • Online & University of Nebraska Omaha, USA (May 28 – May 31, 2024)

2. A generalization of Ito's theorem to skew braces (slides)

   • The Mathematical Society of Japan Autumn Meeting

   • Tohoku University, Japan (Sept 20 – Sept 23, 2023)

3. Regular subgroups in the holomorph, fixed point free pairs of homomorphisms, and group factorizations (slides)

   • Hopf Algebras & Galois Module Theory

   • Online & University of Nebraska Omaha, USA (May 29 – June 2, 2023)

4. Non-abelian simple groups which can occur as the additive group of a skew brace with solvable multiplicative group (slides)

   • Oberwolfach Mini-Workshop: Skew Braces and the Yang-Baxter Equation

   • Online & Oberwolfach Research Institute for Mathematics, Germany (Feb 26 – March 4, 2023)

5. ホップ・ガロア拡大におけるガロア対応 (slides)

   • 15th Research Meeting of Women in Number Theory in Japan

   • Online & Tokyo Institute of Technology, Japan (June 11, 2022)

6. Finite $p$-groups of class two with a very large multiple holomorph (slides)

   • Hopf Algebras & Galois Module Theory

   • Online & University of Nebraska Omaha, USA (May 30  – June 3, 2022)

7. Characterization of the type of Hopf-Galois structures on cyclic extensions (slides)

   • Hopf Algebras & Galois Module Theory

   • Online & University of Nebraska Omaha, USA (May 30  – June 3, 2022)

8. The number of quartic $D_4$-fields with monogenic cubic resolvent ordered by conductor (slides)

   • 32nd Automorphic Forms Workshop

   • Tufts University, Medford, Massachusetts, USA (Mar 19 – Mar 22, 2018)

9. Galois module structure of rings of integers and the Hilbert-Speiser theorem (slides)

   • Number Theory Down Under 5

   • La Trobe University, Bendigo, Australia (Sep 29 – Oct 2, 2017)

10. Galois module structure of the square root of the inverse different in abelian extensions (slides)

    • 14th Meeting of the Canadian Number Theory Association

    • University of Calgary, Canada (June 20 – June 24, 2016)

11. Galois module structure of the square root of the inverse different in abelian extensions (slides)

    • SouthEast Regional Meeting on Numbers XXIX

    • James Madison University, Virginia, USA (April 2 – April 3, 2016)

12. Realizable classes and embedding problems (slides)

    • Joint Mathematics Meetings

    • Washington State Convention Center, Seattle, USA (Jan 3 – Jan 8, 2016)

13. On the Galois module structure of the square root of the inverse different in abelian extensions (slides)

    • Fall Western Sectional Meeting

    • California State University, Fullerton, USA (Oct 24 – Oct 25, 2015)

Presentations at Conferences for Undergraduates, Graduates, and Postdocs

1. Counting binary quartic forms with small Galois group (slides)

   • Yau Mathematical Sciences Center Postdoc Workshop

   • Tsinghua University, Beijing, China (2017) 

2. Galois modules, Adams operations, and the Swan subgroup (notes)

   • Yau Mathematical Sciences Center Postdoc Workshop

   • Tsinghua University, Beijing, China (2016) 

3. Hermitian structure of the square root of the inverse different (notes)

   • Graduate Student Conference in Algebra, Geometry, and Topology

   • Temple University, Philadelphia, USA (May 21 – May 23, 2016)

4. Galois module structure of the square root of the inverse different over maximal orders (slides)

   • Underrepresented Students in Topology and Algebra Research Symposium

   • Sam Houston State University, Houston, USA (April 15 – April 17, 2016)

5. Galois module structure of rings of integers and embedding problems (slides)

   • Symposium for Women in Mathematics in Southern California

   • Pomona College, California, USA (Nov 7, 2015)

6. Galois modules and embedding problems (poster)

   • French-German Summer School on Galois Theory and Number Theory

   • University of Konstanz, Germany (July 18 – July 24, 2015)

7. An overview in the study of Galois modules

   • Underrepresented Students in Topology and Algebra Research Symposium

   • University of California Berkeley, USA (April 11 – April 13, 2014)

8. Galois module structure of abelian extensions

   • Symposium for Women in Mathematics in Southern California

   • University of California Irvine, USA (2013)

Seminar and Colloquium Talks

1. ガロア加群とホップ・ガロア構造と正則部分群 (slides)

   • Friday Tea Time Zoom Seminar, Online (May 27, 2022)

2. The multiple holomorph of centerless groups (slides)

   • Online Seminar, Sun Yat-Sen University (Zhuhai Campus), Guangdong, China (July 15, 2021)

3. Hopf-Galois structures on insolvable extensions (slides)

   • Seminar, Tsukuba University, Japan (Nov 7, 2019) 

4. Isomorphism classes of regular subgroups in the holomorph of a finite group (slides)

   • Seminar, China Jiliang University, Hangzhou, China (Oct 31, 2019) 

5. Hopf-Galois structures and regular subgroups of permutation groups (notes)

   • Seminar, University of Waikato, New Zealand (2018) 

6. Galois module structures and Stickelberger's theorem (slides)

   • Mathematics Seminar, University of Waikato, New Zealand (2018) 

7. The number of quartic $D_4$-fields with monogenic cubic resolvent ordered by conductor (notes)

   • Number Theory Seminar, University of Oxford, UK (May 17, 2018)

8. Construction of Hopf-Galois structures via regular subgroups of permutation groups (notes)

   • Number Theory Seminar, University of Exeter, UK (May 15, 2018) 

9. The number of quartic D_4-fields with monogenic cubic resolvent ordered by conductor (notes)

   • Colloquium, University of Hong Kong, Hong Kong (March 5, 2018)

10. Binary quartic forms with bounded invariants and small Galois groups (notes)

    • Postgraduate Student Number Theory Seminar, University of Hong Kong, Hong Kong (Feb 15, 2017)

11. Normal integral basis and embedding problems (notes)

    • Seminar, Keio University, Japan (2015)

Departmental Talks 

At Sun Yat–Sen University, Zhuhai Campus, China

1. Isomorphism types of regular subgroups in the holomorph of a finite group (notes) (2020) 

2. An introduction to the study of the multiple holomorph of groups (notes) (2019) 

3. Fixed point free pairs of endomorphisms on a direct product via graph theory (notes) (2019) 

4. Galois module structures and Hopf-Galois structure (notes) (2018) 

At University of California Santa Barbara, USA

5. Navigating in $F_p$ and generalized Fibonacci numbers (notes) (2016) 

6. Hermitian structure of the square root of the inverse different (notes) (2016)

7. Introduction to abelian class field theory (notes) (2016)

8. Classical Iwasawa theory and $Z_p$-extensions (notes) (2016) 

9. The inverse Galois problem over Q (notes) (2015) 

10. Diophantine equations and the Hasse principle (notes) (2015) 

11. Galois modules and embedding problems (notes) (2015) 

12. Primes of the form $x^2+ny^2$ (notes) (2014) 

13. Introduction to supercharacters and superclasses (notes) (2014) 

14. Realizable classes and tame abelian extensions (notes) (2014) 

15. Galois modules and realizable classes (notes) (2013) 

16. Public-key, private-key, and quantum cryptography (notes) (2013) 

17. Existence of a normal integral basis and ramification (notes) (2013) 

18. A brief review on tensor product of modules (2013)

19. An overview of valuation theory (2012)

20. Infinite Galois theory and profinite group topology (2012)