**Lecture Notes**

Calabi-Yau property under monoidal Morita-Takeuchi equivalence

Poisson geometry in noncommutative algebra

Poisson geometry in noncommutative projective algebraic geometry

Quantum symmetry in noncommutative projective algebraic geometry

Noncommutative symmetric groups in noncommutative projective algebraic geometry

Quantum groups associated to a pair of regular forms

The relation between Calabi-Yau property and unimodularity for Poisson algebras

Homological unimodularity and Calabi-Yau condition for Poisson algebras

Primitive deformation and classification of Hopf algebras up to prime-cube dimension

**Talk Slides**

Enveloping algebras of double Poisson-Ore extensions

Classification of connected Hopf algebras up to prime-cube dimension

Isomorphism classes of small quantum groups in positive characteristic

Classification of small unipotent quantum groups in positive characteristic and its applications

Connected Hopf algebras in positive characteristic

Finite-dimensional connected Hopf algebras

**Invited Talks: Conferences and Research Seminars**

AMS Special Session on Homological Aspects of Noncommutative Algebra and Geometry, San Francisco State University, San Fransisco, CA, October 2018.

Joint International Meeting of the American and Chinese Mathematical Societies, Special Session on Noncommutative Algebra and Related Topics, Fudan University, Shanghai, China, June 2018.

Algebra and Combinatorics Seminar, Texas A&M University, College Station, TX, April 2018.

AMS Special Session on Hopf Algebras, Tensor Categories, and Homological Algebra, Northeastern University, Boston, MA, April 2018.

AMS Special Session on Noncommutative Algebra and Representation Theory, Northeastern University, Boston, MA, April 2018.

AMS Special Session on Noncommutative Algebraic Geometry and Related Topics, Portland State University, Portland, OR, April 2018.

AMS Special Session on Noncommutative Algebra and Noncommutative Algebraic Geometry, Ohio State University, Columbus, OH, March 2018.

Noncommutative algebra from a geometric point of view. Algebra Seminar, University of Buffalo, Buffalo, NY, February 2018.

Noncommutative algebra from a geometric point of view. Colloquium, George Mason University, Fairfax, VA, February 2018.

Noncommutative algebra from a geometric point of view. Colloquium, Embry-Riddle Aeronautical University, Prescott, AZ, February 2018.

AMS Special Session on Noncommutative Algebras and Noncommutative Invariant Theory, San Diego, CA, January 2018.

Calabi-Yau property under monoidal Morita-Takeuchi equivalence. Special Session on Noncommutative and Homological Algebra, University of North Texas, Denton, TX, September 2017.

Universal enveloping algebras of double Poisson-Ore extensions. Special Session on Topics Related to the Interplay of Noncommutative Algebra and Geometry, University of North Texas, Denton, TX, September 2017.

Calabi-Yau property under monoidal Morita-Takeuchi equivalence. Algebra Extravaganza-a conference in honor of Ellen Kirkman and Martin Lorenz, Temple University, Philadelphia, PA, July 2017.

The Poisson geometry of the 3-dimensional Sklyanin algebras. Special Session on Noncommutative Algebraic Geometry and Related Topics, Washington State University, WA, April 2017.

Poisson geometry in noncommutative algebras. Algebra, Combinatorics and Geometry Graduate Student Research Seminar, University of Pittsburgh, Pittsburgh, PA, March 2017.

Poisson geometry of 3-dimensional Sklyanin algebras. Fudan-Guanghua International Forum for Young Scholars in Mathematics, Fudan University, Shanghai, China, March 2017.

Quantum symmetry in noncommutative algebra. Colloquium, University of Denver, Denver, CO, January 2017.

Non-noetherian Hopf algebras versus noetherian Hopf algebras. AMS Special Session on New Developments in Noncommutative Algebra & Representation Theory, Atlanta, GA, January 2017.

Quantum groups associated to a pair of preregular forms. AMS Special Session on Hopf Algebras and their Actions, Atlanta, GA, January 2017.

Homological unimodularity and Calabi-Yau condition for Poisson algebras. AMS Special Session on Quantum Algebra, University of Denver, Denver, CO, October 2016.

Homological unimodularity and Calabi-Yau condition for Poisson algebras. AMS Special Session on Noncommutative Ring Theory and Noncommutative Algebra, Bowdoin College, Brunswick, ME, September 2016.

Poisson Geometry and noncommutative algebra. Poisson Algebra Workshop, Zhejiang Normal University, Jinhua, China, July 2016.

Quantum symmetry in noncommutative projective algebraic geometry. Algebra Seminar, Anhui University, Hefei, China, June 2016.

Poisson geometry in noncommutative projective algebraic geometry. Algebra seminar, University of Science and Technology of China, Hefei, China, June 2016.

Noncommutative symmetric groups in noncommutative projective algebraic geometry. Algebra seminar, Suzhou University, Suzhou, China, June 2016.

Primitive deformation and classification of Hopf algebras up to prime-cube dimension. Algebra seminar, Zhejiang University, Hangzhou, China, June 2016.

Quantum groups associated to a pair of pre-regular forms. Hopf Algebra and Actions Workshop Part II, University of Washington, Seattle, WA, April 2016

Noncommutative symmetric groups in noncommutative projective algebraic geometry. Algebra seminar, University of Pittsburgh, Pittsburgh, PA, March 2016.

Noncommutative symmetric groups in noncommutative projective algebraic geometry. Algebra seminar, Northeastern University, Boston, MA, February 2016.

Primitive deformations of quantum p-groups II. Algebra Seminar, Temple University, Philadelphia, PA, April 2016.

Primitive deformations of quantum p-groups I. Algebra Seminar, Temple University, Philadelphia, PA, March 2016.

Universal enveloping algebras of Poisson-Ore extensions. Joint Mathematics Meeting, Seattle, WA, January 2016.

Quantum p-groups and their classification in low dimensions. Algebra Seminar, Louisiana State University, Baton Rouge, LA, November 2015.

Noncommutative symmetric groups in noncommutative projective algebraic geometry. Algebra seminar, Temple University, Philadelphia, PA, October 2015.

On quantum groups associated to non-noetherian regular algebras of dimension 2. Seattle noncommutative algebra day, University of Washington, Seattle, WA, August 2015.

On quantum groups associated to non-noetherian regular algebras of dimension 2. Hopf Algebra and Tensor Category Mini-Meeting, University of Southern California, Los Angeles, CA, May 2015.

On quantum groups associated to non-noetherian regular algebras of dimension 2. Hopf algebra seminar, University of Southern California, Los Angeles, CA, April 2015.

Universal enveloping algebras of Poisson algebras. Algebra Seminar, University of California at San Diego, San Diego, CA, February 2015.

Classification of connected Hopf algebras up to prime-cube dimension. Joint Mathematics Meeting, San Antonio, TX, January 2015.

Isomorphism classes of Hopf algebras in positive characteristic. Algebra Seminar, University of California at San Diego, San Diego, CA, September 2014.

Small unipotent quantum groups arising from primitive control deformation. Hopf Algebra Seminar, University of Southern California, Los Angeles, CA, September 2014.

Classification of small unipotent quantum groups in positive characteristic and its applications. Algebra Seminar, University of Southern California, Los Angeles, CA, September 2014.

Connected Hopf algebras in positive characteristic. Algebra Seminar, University of Pittsburgh, Pittsburgh, PA, November 2013.

Finite-dimensional connected Hopf algebras. AMS Special Session on Recent Developments in Noncommutative Algebra, Temple University, Philadelphia, PA, October 2013.