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Geometric Aspects of Quantum Dualities

 I. Coordinator:
  • Prof. Siye Wu (Department of Mathematics, NTHU)


II. Core Members:

  • Prof. Nan-Kuo Ho (Department of Mathematics, NTHU)
  • Prof. Chong-Sun Chu (NCTS & Department of Physics, NTHU)
  • Prof. Pei-Ming Ho (Department of Physics, NTU)
  • Dr. Sheng-Fu Chiu (postdoc, Institute of Mathematics, Academia Sinica)
  • Mr. Chin-Chia Chang (master student, Department of Mathematics, NTHU) 

 

III. Research Themes:

  • The proposed research will be on the dualities in gauge theory and in sigma-models, and their mathematical consequences, especially in geometry. One theme is dualities in N = 2 and N = 4 SUSY gauge theories. We plan to explore its manifestations in a number of settings, including putting gauge theories on di erent spacetime manifolds, of di erent twists (in the case of N = 4) and for simply and non-simply laced gauge groups. The mathematical concepts involved are instanton moduli space, moduli space of  at connections, Hitchin integrable system, non-orientable surfaces, Langlands duality, Seiberg-Witten, Vafa-Witten and Kapustin-Witten equations. Most core members have worked on one or more aspects in the above. Another theme is sigma-model with target spaces of various geometries, especially generalised geometry and geometric with  ux backgrounds. We plan to explore Kahler, hyper-Kahler and Calabi-Yau manifolds in these generalised contexts and their mirror symmetry, T-duality.
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  • It is important to keep the interaction alive between the two major theoretical communities: mathematics and high energy physics in Taiwan. If funded, the proposed activities can help mathematicians understand physics origin and points of view and physicists work out and test their ideas with powerful mathematical tools and pose more challenging conjectures to mathematicians. Some overseas scienti c communities are already much more advanced in forging such fruitful interactions, and this is clearly re ected in the publications of their members. By inviting experts from overseas to give lectures and for collaboration, we keep taiwan well connected to the international scene. 


IV. Tentative plan of activities:

  • In the first year (2019), we plan to organise regular discussions meetings and small lecture series with local and international visitors. These involve lectures or talks with a mixture of mathematics and physics, but related topics. 
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  • The activities in the second year (2020) will be built on the basis of the previous year and will be more in-depth. Also, instead of having small events, we plan to have a medium size workshop with two international speakers. With the budget constraint, we plan to invite one from Asia and one from Europe or North America. 

 

VExpected achievements:

  • The proposed activities can achieve in several aspects. First, they will produce scienti c publications of core members and their collaborators in mathematical physics that are competitive internationally. Second, since the activities are open to all, they will inspire those who wish to know the general area but not necessarily to do research in these areas. Finally, the postgraduate students, postdoctoral members and young researchers can bene t from the programme and start their research with fresh ideas from the very beginning.
 

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