#  Seminar: Alina Vdovina (City College of New York and Graduate Center, CUNY): "Higher dimensional digraphs from cube complexes and their spectral theory" 

 



####  calendar\_today Date and Time 

 **November 14, 2023** 

 09:30AM - 09:30AM EST 

####  pin\_drop Location 

 **Jefferson 453 and Zoom**  



 

 



 

   ![Alina Vdovina](/sites/g/files/omnuum6611/files/styles/hwp_1_1__360x360_scale/public/mathpicture/files/alinavdovina.jpg?itok=roemzSue) 

 

  
Zoom link: <https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09>  
Speaker: Alina Vdovina (City College of New York and Graduate Center, CUNY)  
Title: **Higher dimensional digraphs from cube complexes and their spectral theory**  
Abstract: We define k-dimensional digraphs and initiate a study of their spectral theory. The k-dimensional digraphs can be viewed as generating graphs for small categories called k-graphs. Guided by geometric insight, we obtain several new series of k-graphs using cube complexes covered by Cartesian products of trees, for k≥2. These k-graphs can not be presented as virtual products, and constitute novel models of such small categories. The constructions yield rank-k Cuntz-Krieger algebras for all k≥2. We introduce Ramanujan k-graphs satisfying optimal spectral gap property, and show explicitly how to construct the underlying k-digraphs.

 

 



 

 

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