Talks

Past Lectures

1. An introduction to nonsemisimple topological quantum compiling", Joint Meeting of the AMS,  Session on Modular tensor categories and TQFTs beyond the finite and semisimple San Francisco, January 5th-6th.

2. "An introduction to nonsemisimple topological quantum compiling", Merging Categorification, Gauge Theory, and Physics, Hotel Belalp, Swiss Alps, September 3rd - 8th, 2023

3. "Heegaard Floer Homology as a quantum invariant," 2023 Simons Collaboration on New Structures in Low-Dimensional Topology Annual Meeting, Simons Foundation, New York, NY, March 30-31, 2023

4. "Categorification Meets the Amplituherdon," Hidden Mathematical Structures of the Amplituhedron, Dublin Institute for Advanced Study, Dublin, Ireland, April 24-28, 2023

5. "Derived super equivalences from odd categorified quantum groups" (video),  Categorification in representation theory, University of Sydney, February 13-17th, 2023

6. Lattice models arising from nonsemisimple TQFT (video), From Subfactors to Quantum Topology - In memory of Vaughan Jones, University of Geneva, Geneva, Switzerland June 27th - July 1, 2022

7. "Skew Howe duality and knot homology", KLR-algebra seminar, Columbia University, April 25th, 2022

8. "Derived super equivalences from odd categorified quantum groups" (video), Braids in Representation Theory and Algebraic Combinatorics, ICERM, February 14th - 18th, 2022

9. "Non-semisimple TQFT and topological phases", Plenary Speaker with Nati Seiberg, Caltech Idea Incubator, Caltech Marth 12th, 2022

10. Representation Theory, Oberseminar, Bonn, Germany,  February 5th, 2021 [Virtual due to COVID]

11. Four-part lecture series, East China Normal University December 2020 

12. USC Physics Department Colloquium, November 18th, 2020

13. Plenary Address, The Eighth Pacific Rim Conference in Mathematics, U.C. Berkeley, August 3rd-7th, 2020 [CANCELED due to COVID] 

14. QUAntum groups, Categorification, Knot invariants, and Soergel bimodules, University of Oregon, August 10th-14th, 2020 [CANCELED due to COVID]  

15. "A new look at quantum knot invariants ", Mathematics Department Colloquium, Ohio State University, February 20th, 2020  

16. "Bordered Heegaard-Floer homology, category O, and higher representation theory ", Quantum Algebra & Quantum Topology (QAQT) seminar, Ohio State University, February 20th, 2020

17. "What is Categorification", Graduate student pre-seminar lecture, Ohio State University, Ohio State University, February 20th, 2020 

18. Introductory Workshop: Higher Categories and Categorification, MSRI, Berkeley, California, February 10-14th, 2020 

    1. An introduction to categorification of quantum groups and link invariants I

    2. An introduction to categorification of quantum groups and link invariants II

    3. An introduction to categorification of quantum groups and link invariants III

19. "Bordered Heegaard-Floer homology, category O, and higher representation theory ", Geometry and Representation Theory,   UC Riverside,  December 14th-16th, 2019. 

20. "Bordered Heegaard-Floer homology, category O, and higher representation theory ", Algebraic and Geometric Categorification (19w5074),  Banff International Research Station for Mathematical Innovation and Discovery  of Casa Matemática Oaxaca , Mexico,  December 1 -6, 2019 

21. "Bordered Heegaard-Floer homology and higher representation theory", Algebra seminar, University of Oregon, November 26th, 2019 

22. "A new look at quantum knot invariants", Mathematics Colloquium, University of Oregon, November 25th, 2019 

23. "Bordered Heegaard-Floer homology, category O, and higher representation theory", AMS Special Session on Geometry and Representation Theory of Quantum Algebras and Related Topics, UC Riverside,  November 9-10th, 2019

24. Quiver Hecke Algebra and its applications to topology, Nagoya, Japan, July 7-11, 2019

    1. "An introduction to categorification of quantum sl(2)" 

    2. "The Howe duality revolution and unexplored frontiers"

25.  Two-part graduate student lectures,  Moab Topology Conference,   Moab, Utah. May 9-11, 2019

    1. "A new look at Quantum Categorification" 

    2. "Categorified quantum knot invariants from higher representation theory"

26. "The Howe duality revolution and unexplored frontiers",  Hidden Algebraic Structures in Topology, Caltech,  March 14 - 16, 2019

27. "An introduction to quantum categorification",  Higher symmetries, Aspen Center for Physics, March 17-22, 2019

28. "Current algebras and categorification", Interactions of quantum affine algebras with cluster algebras, current algebras and categorification dedicated to Professor Vyjayanthi Chari on her 60th birthday, Catholic University of America, Washington D.C,  June 2 - June 8, 2018. 

29. "An introduction to quantum categorification", TQFT and Categorification, Institut d'Etudes Scientifiques de Cargese, France, April 16th -- 20th, 2018 

30. "Towards a quantum construction of Alexander categorifications and related spectral sequences",  Quantum knot homology and supersymmetric gauge theories, Aspen Center for Physics, March 4-10, 2018

31. "A new look at quantum knot invariants",  Brandeis-Harvard-MIT-Northeastern Joint Mathematics Colloquium, February 22nd, 2018

32. "Diagrammatic Algebra", Undergraduate lecture, Northeastern University, February 19th, 2018

33. "Higher categories and two-dimensional topology ", Undergraduate lecture, Northeastern University, February 19th, 2018

34. “A new look at quantum knot invariants”,  Mathematical Physics Seminar, UC Berkeley, April 3rd, 2017. 

35. “A new look at quantum knot invariants”, Math Department Colloquium, Columbia University,  November 30th, 2016.

36. “An introduction to odd symmetric functions”, Combinatorics Seminar, USC, November 16th, 2016

37. “A new look at quantum knot invariants”, Math Department Colloquium, UCLA, November 10th, 2016

38. “Beyond quantum knot invariants via categorification”,  Math Department Colloquium, UCR,  October 19th, 2016

39. “Odd structures arising from categorified quantunm groups”, Homological Methods in Algebra and Geometry, AIMS Ghana, August 1st- 5th, 2016.

40. “Introduction to categorified quantum groups” (two lectures), Diagrammatics and Topology, Okinawa, August 3rd - 7th, 2015.  

41. “Interactions between knot theory and theoretical physics”, International Congress of Mathematical Physics, Santiago, Chile, July 27th, 2015. 

42. “Traces and diagrams on the annulus”, Algebra and Geometry Seminar, Melbourne University, Melbourne Australia, July 3rd, 2015

43. Categorification in Algebra, Geometry and Physics (A conference in honor of the 60th Birthday of Christian Blanchet), IESC, Menasina, Cargese, France,  May 4-8th, 2015

44. “Knot invariants and their categorifications via Howe duality”, Geometry and Topology seminar, Georgia Tech University, April 12th, 2015.  

45. Traces and diagrams on the annulus”, Mathematics Colloquium, Louisiana State University, March 17th, 2015. 

46. "From ladder diagrams to knot theory”, Graduate student Colloquium, LSU March 17th, 2015.

47. “Diagrammatic algebra”, Undergraduate Colloquium, LSU, March 16th, 2015.

48. “Planar diagrams on the annulus and the algebraic Chern character”,  Lie theory seminar,  Riverside, CA February 6th, 2015.

49. "Odd structures arising from categorified quantum groups", Categorical Methods in Representation Theory, AMS Fall meeting, San Francisco State University, October 25-26th.

50. “Current algebras form categorified quantum groups” , ICM Satellite Conference on Representation Theory and Related Topics, Daegu Korea, August 6-10th, 2014

51. “Knot invariants and their graphical calculus via Howe duality”, Quantum Topology, Chelyabinsk, Russia, July 10, 2014

52. “Categorified knot invariants from categorified Howe duality”, Quantum Topology, Chelyabinsk, Russia,  July 11th, 2014

53. “Odd structures arising from categorified quantum groups”, University of Zurich, July 1, 2014

54. .“Current algebras from categorified quantum groups”, Categorification and geometric representation theory, CRM, Montreal, June 9--13, 2014.

55. “The odd cohomology of Springer varieties and the Hecke algebra at q=-1,” Algebra seminar,  La Spienza University, Rome, March 4th, 2014

56. “Categorification and diagrammatic algebra”, Mathematics colloquium, University of Geneva, February 11th, 2014

57. “Categorification and diagrammatic algebra”, Mathematics colloquium, University of Madison Wisconsin, January 6, 2014

58. “Odd structures arising from categorified quantum groups”, Categorification workshop, Paris 7, December 5, 2013

59. “Categorification and diagrammatic algebra”, Mathematics colloquium, Temple University, December 2, 2013

60. “Categorification and diagrammatic algebra”, Mathematics colloquium, University of Melbourne, October 15, 2013

61. “Knot invariants and their categorifications via Howe duality”,  Physics and Mathematics of Link Homology, Séminaire de Mathématiques Supérieures, Montréal,  June 24--July 5, 2013.

62. “Knot invariants and their categorifications via Howe duality”,  Representation theory and categorification, Pacific Rim Mathematical Association, Jiaotong University, Shanghai, China, June 24th - June 28th, 2013.

63. “Knot invariants and their categorifications via Howe duality”, Young women in topology, Bonn, Germany,  June 7th-9th, 2013. 

64. "Getting knot invariants from representation theory via Howe duality” , Quantum topology and related topics, Nha Thang, Vietnam,  May 13th-17th, 2013.

65. `` Getting knot invariants from representation theory via Howe duality” , Southern California Algebra Conference,  UCLA, April 27th, 2013.

66. `` Getting knot invariants from representation theory via Howe duality”, Mapping class groups and categorification, Banff International Research Station, April 7th-12th, 2013.

67. “A new look and knot invariants arising from representation theory with a via towards categorification”, German Research Council program in Representation Theory, March 25th-28th,  Bad Boll, Germany, 2012.

68. “Odd structures arising from categorified quantum groups” , Lie algebras, algebraic transformation groups, and representation theory, Joint Mathematics Meetings in San Diego, CA, January 9th-12, 2013.

69. “From skew Howe duality to knot invariants”, Groups, representations,  and applications, Joint AMS Meetings in San Diego, CA, January 9th-12th, 2013.

70. “From skew Howe duality to knot invariants”, Algebra and Lie Theory seminar, CU Boulder, November 27th, 2012.

71. “An introduction to odd symmetric functions”, UCLA Combinatorics seminar, November 1st, 2012.

72. “Crystals and categorification” , USC Combinatorics seminar, October 29th, 2012

73. “Odd structures arising from categorified quantum groups”, Quantum Groups and Noncommutative Algebraic Geometry,  Fall Western Section Meeting of the AMS, Tulane University, New Orleans, October 13-14, 2012.

74. Gradings and decomposition numbers, University of Stuttgart, Germany,  September 24-28th, 2012 .

    1. ◦“Odd structures arising from categorified quantum groups”,

    2. ◦“The odd cohomology of Springer varieties and the Hecke algebra at q = −1”

75. “Categorical Lie algebra actions and skew Howe duality” (two lectures), Higher Structures in China III, August 13-19th, 2012.

76. “What is a category?”, REU Colloquium,  Cal State Channel Islands,  July 11th, 2012.

77. “Categorification of quantum groups”, Algebra Colloquium, East China Normal University, Shanghai, May 21st, 2012.

78. “Lectures on categorified quantum groups” (10 lectures), East China Normal University, Shanghai, May 4th - May 24th, 2012.

79. “Odd structures arising from categorified quantum groups”, George Washington University, Washington D.C, May 1st, 2012. 

80. Southeastern Lie Theory conference,  North Carolina State University, April 21-22, 2012.

    1. "Categorical Lie algebra actions and quantum groups”,  April 21st, 2012

    2. “Odd structures arising from categorified quantum groups”, April 22nd, 2012

81. “Categorifying quantum groups using planar diagrammatics”, Penn State Applied Algebra Seminar, March 21, 2012. 

82. “Towards odd Khovanov homology via categorified quantum groups”, AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory, Tampa Florida, March 10-11, 2012.

83. “The odd nilHecke algebra and categorified quantum sl(2)”, AMS Special Session on Interactions between algebraic combinatorics and representation theory, Tampa Florida, March 10-11, 2012.

84. “Towards odd Khovanov homology via categorified quantum groups”, L.A. Topology Seminar, November 28th, 2011.

85. “Odd categorification and cohomology”, Southern California Algebraic Geometry seminar, UCLA, November 5th, 2011.

86. “The odd nilHecke algebra and categorified quantum sl(2)”, Workshop on Category Theoretic Methods in Representation Theory, University of Ottawa, October 14-16, 2011.

87. “String diagrams and 2-categories”, Topology working seminar, USC, September 20th, 2011.

88. “The odd nilHecke algebra”, Algebraic Lie theory, Cambridge Isaac Newton Institute, Cambridge, UK, September 12-16, 2011.

89. "Diagrammatic categorification of quantum groups" (two lectures), University Paris Diderot, PPS Seminar, May 30th, 2011.

90. "The structure of categorified representation theory", Swiss Knots 2011, Lake of Thun, Switzerland, May 22-28, 2011.

91. Universitat Zurich, May 13th and May 20th, 2011.

    1. ◦"The nilHecke algebra and categorified quantum sl2",

    2. ◦"Beyond the nilHecke algebra: categorifying Kac-Moody algebras",

92. "From partial flag varieties to categorification of quantum sl2", ETH Zurich, May 5th, 2011.

93. "From cohomology of Grassmannians to categorification of sl(2)", LSU, Algebra seminar, April 12th, 2011.

94. "From cohomology of Grassmannians to categorification of sl(2)", University of Southern Alabama, Algebra seminar, March 25th, 2011.

95. "Diagrammatic categorification of quantum groups", Colloquium, Georgia Tech, January 26th, 2010.

96. "Categorifying quantum groups and link invariants", University of Georgia, January 25th, 2010.

97. "Categorifying quantum groups and link invariants", LSU Colloquium, January 21st, 2010.

98. "Categorifying quantum groups and link invariants", UCSD Math Colloquium, January 17th, 2010.

99. "Inventing KLR algebras", Taipei Conference on Representation Theory in Academia Sinica, Taipei, Taiwan, December 19-23, 2010.

100. "Diagrammatic categorification of quantum groups", Colloquium, Purdue University, December 10th, 2010.

101. "Diagrammatic categorification of quantum groups", Northeastern GASC seminar, November 29th, 2010.

102. "Diagrammatic categorification of quantum groups", USC Geometry and Topology Seminar, November 22nd, 2010.

103. "Diagrammatic categorification of quantum groups", Colloquium, Boston College, November 19th, 2010.

104. "Diagrammatic categorification of quantum groups",  CUNY Representation Theory Seminar, November 12th, 2010

105. "Quantum knot invariants and their categorifications", Graduate student topology seminar, LSU, October 29th, 2010.

106. "Diagrammatic categorification of quantum groups" (four lectures), Higher Structures 2010, Erwin Schroedinger Institute (ESI), Vienna, October 19-22, 2010.

107. "Categorifying quantum sl2", UPenn Math/Physics Seminar, October 12th, 2010.

108. Algebraic and Combinatorial Approaches to Representation Theory, Indian Institute of Science, Bangalore, India, August 12th-16th 2010.

109. "Diagrammatic approach to categorification of quantum groups" (three lectures), XIXth Oporto Meeting on Geometry, Topology, and Physics, Portugal, 19-23 July 2010.

110. Categorification of topological invariants and applications, Stony Brook, June 21st-25th, 2010.

111. Double Affine Hecke Algebras and Algebraic Geometry Workshop, MIT, May 17th-21st, 2010.

112. "Categorifying quantum groups", Rutgers, Lie Groups and Quantum Math Seminar, April 30th, 2010.

113. "Categorifying quantum sl2", Homology Theories of Knots and Links, MSRI Berkeley, March 15th-19th, 2010.

114. "Diagrammatic algebra", Manhattan College, February 9th, 2010.

115. "Categorifying quantum groups", Geometry, Symmetry and Physics seminar, Yale University, February 4th, 2010.

116. "Diagrammatic categorification of quantum groups", Introductory workshop: Homology Theories of Knots and Links, MSRI Berkeley, January 25th - 29th, 2010.

117. "A categorification of quantum sl(2)", Introductory workshop: Homology Theories of Knots and Links, MSRI Berkeley, January 25th - 29th, 2010.

118. "Categorifying quantum groups", AMS special session "Cohomological and algebraic methods in representation theory", National AMS meeting in San Francisco, California, January 13th - 16th, 2010.

119. "Categorifying quantum sl2", Knots in Washington XXIX, George Washington University, December 4-6, 2009

120. "Categorifying quantum groups", AMS special session "Homotopy theory and higher algebraic structures", AMS Western Section Meeting, University of California, Riverside, Novermber 7-8th 2009.

121. "Categorifying quantum groups", International workshop on Lie algebras and related topics, NIMS, Daejon, Korea, October 19-22, 2009.

122. "Categorifying quantum groups", New York Area Algebra Seminar, CUNY Graduate Center, October 9th, 2009.

123. "Categoriying quantum sl2", Institute for Mathematics, University of Zurich, July 30th-August 9th, 2009.

124. "Categoriying quantum sl2", Combinatorial Geometric Structures in Representation Theory, London Mathematical Society Durham Symposium, July 6th - July 16th, 2009.

125. "Categoriying quantum sl2", Summer School on Link homology, Institut Henri Poincaré, Paris June 29th -- July 3rd, 2009.

126. "Categorifying quantum groups", Geometric Representation Theory and Extended Affine Lie Algebras, University of Ottawa, June 29 - July 3, 2009. (pdf slides)

127. "Categoriying quantum sl2", Algebra and Discrete Mathematics Seminar, University of California Davis, May 14th-21st, 2009

128. "Categorifying quantum sl2", Categorification and Geometrisation from Representation Theory University of Glasgow, April 13 -18, 2009

129. "Categorifying quantum groups", 88th Peripatetic Seminar on Sheaves and Logic , Cambridge University, April 4-5, 2009.

130. "A categorification of quantum sl(2)", Nagoya University, January 20th, 2009

131. "Lectures on categorified quantum groups" (three lectures), Kyoto University, Japan January 15th - January 27th, 2009

132. "Categorifying quantum groups", Knots in Washington,  Colloquium George Washington University, January 9-11, 2009.

133. "Diagrammatic algebra", Graduate Colloquium, George Washington University, December 8th, 2009.

134. ."Categorifying quantum groups", Representation Theory, Geometry & Combinatorics Seminar, Berkeley, October 6th, 2008.

135. "Categorifying quantum groups", Combinatorial Representation Theory, Fall Western Section Meeting of the AMS, University of Britsh Columbia and PIMS, Vancouver, October 4--5, 2008.

136. "Frobenius algebras and Topological Quantum Field Theory", Undergraduate Mathematics Society, Columbia University, September 17th, 2008.

137. "Categorifying quantum groups", Symplectic geometry seminar, Columbia University, September 12th, 2008.

138. "Categorifying quantum groups", QG2 2008 Quantum Geometry and Quantum Gravity Conference , Nottingham, July 2nd, 2008

139. Link homology and categorification, Kyoto

     1. ◦"Jones polynomial and its extension to tangles", May 10th, 2007

     2. ◦"A homological invariant of tangles and tangle cobordisms", May 11th, 2007

     3. ◦"sl(3) link homology", May 11th, 2007

140. "Quantum topology and tangle homology", University of California, Riverside, February 2007

141. "Frobenius algebras, quantum topology and higher categories", Thematic Program on Geometric Applications of Homotopy Theory, Fields Institute, Toronto, January13th, 2007

142. "Open closed TQFTs and tangle homology", Geometry/Topology Seminar, Columbia University, October 2006.

143. "The topology of open and closed strings", The Invariant Society, University of Oxford, May 16th, 2006.

144. "Open-closed TQFTs and tangle homology", two talks joint with Hendryk Pfeiffer, University of Chicago, April 2006.

145. "Khovanov homology and open-closed TQFTs", Homotopy Theory Mini-conference, Sheffield, January 13th 2006.

146. "Khovanov's categorification of the Jones polynomial", Max Planck Institute for Gravitational Physics, Potsdam, December 8th 2005.

147. "From adjunctions to extended TQFTs", Topology Seminar, University of Oxford, November 28th, 2005.

148. "Frobenius algebras and thick tangles", Pure Mathematics Colloquiums, University of Sheffield, November 23rd,  2005.

149. "Constructing functors from string worldsheets into algebraic categories.", Categories and Logic Seminar, University of Cambridge, November 15th 2005.

150. "Frobenius algebras and thick tangles", Joint Algebra and Geometry/Topology Seminar, University of Glasgow, November 2nd 2005.

151. "Worldsheet topology and state sum models", Math/Phys Learning Seminar, Stony Brook University, October 24th, 2005.

152. "Frobenius algebras and thick tangles", Quantum Gravity Seminar, University of California, Riverside June 2005.

153. "From physics to functors", two talks, Category Theory Seminar, University of Chicago, May 2005.

154. "Frobenius algebras and thick tangles", Topology Seminar, University of Chicago, May 2005.

155. "Frobenius algebras and topological quantum field theory", Seminars for Undergraduates Too , Subgroup of the University of Cambridge Archimedeans, February 2005.

156. "2-Groups, trialgebras and Hopf Categories", two talks with Richard Garner and Henry Pfeiffer, Categories and Logic Seminar, University of Cambridge, January/February 2005.

157. "An introduction to Khovanov homology", Categories and Logic Seminar, University of Cambridge, October 2004.

158. "Frobenius Categories", Summer Topology Seminars, University of California San Diego, September 2004.

159. " Categorified Frobenius Algebras", Oporto Meetings on Geometry, Topology and Physics, July 2004.

160. "Frobenius Algebras and the Walking Ambidextrous Adjunction", Categories and Logic Seminar, University of Cambridge, March 2004.

161. "Internalization", Topology Seminar , Norwegian University of Science and Technology, December 2003.

162. "String Diagrams and 2-Groups", Topology Seminar , Norwegian University of Science and Technology, December 2003.

163. "2-Groups and String Diagrams", Categories and Logic Seminar, University of Cambridge, October 2003.

164. "Categorified Groups", Quantum Gravity Seminar, University of California, Riverside, April 2003.