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Static Knot Energy, Hopf Charge, and Universal Growth LawPowerPoint Presentation

Static Knot Energy, Hopf Charge, and Universal Growth Law

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### Static Knot Energy, Hopf Charge, and Universal Growth Law

(joint work with Fanghua Lin)

Yisong Yang

Polytechnic University

Talk given at the Chern Institute conference “Topology and Physics” in memory of Xiaosong Lin

July 27 – 31, 2007

Xiaosong’s influence outside his specialty area (low dimensional topology and knot invariants)

Got to know Xiaosong during 1993-1994 at IAS dimensional topology and knot invariants)

Initial impressions about XS:

A person of high intellectual pursuit

An inspiring educator

Genuine

A gentleman of soft voice and smile

(these impressions never changed over time)

Later encounters: conferences dimensional topology and knot invariants)

Two most notable conferences XS and I had together are

The 2nd Sun Zi Institute Conference at Rutgers in 1995

The 23rd International Conference on Differential Geometry Methods in TheoreticalPhysics at Nankai in 2005

Title of Rutgers Talk: Knot Energies and Knot Invariants (1995)

Xiaosong’s opening words: “Knots are fascinating objects.”

Based on this talk, Xiaosong wrote a beautiful survey article under the same title (presenting historical developments and current state of art of the subject)

See: http://arxiv.org/PS_cache/q-alg/pdf/9604/9604018v1.pdf

Added impressions: A leader and an ambassador of knot theory

Nankai Conference 2005 (1995)

Had numerous discussions with Xiaosong on the knot study Fanghua Lin and I were doing

In particular, Xiaosong told us about the work of some knot theory people on “ideal knots” related to our work (in particular, that of Canterella, Kusner, and Sullivan; Buck)

Extensive email exchanges lasted until May 6, 2006 (often long and precise)

August, 2005

Last Email From Xiaosong Dated 05/06/2006 (1995)

Thank you very much for sending me this nice survey. It is my hope to getto know this subject better and communicate your work to the knot theorycommunity.Best regards,Xiao-Song

Email of Fanghua Lin on Xiaosong (1995)

Xiaosong and I met only a few times in person, but impressions aredeep. We shared the same last name (so God knows we may be connected through a simple homotopy - that was a joke we used to make).What I admire Xiaosong most is not his mathematics (I knew he was one of thebest in his business if not the best) because I did not know his stuffwell. I admire his honesty and straightforwardness toward friends andcolleagues. Always a very sincere, trustable and reliable friend.

At the 1997 Bekerley meeting (by NSF China, in honor of Chern), we decided tohave a journal “Comm. in Contem. Math". I was asked to be co-chief editor. But due to my many commitments, I turned it down. Instead I suggested Luis Caffarelli (he could not do it either). Then I suggested Haim Brezis. Thinking back, I feel bad as it gave a lot of work to Xiaosong. Hemade the journal very successful within a few years. As an editor, I didhelp him with a lot of work as well as handling some difficultcases. Through these occasions, I got to know Xiaosong better. Tothis day, I still miss him terribly as a colleague and a friend.But he will always be remembered. Best,

Fanghua

PS. I am glad you are there for this event. Our latest work owes also to Xiaoong's input.

Faddeev Knots: Existence of Knots from the First Principle (1995)

Numerical work of Battye and Sutcliffe

Faddeev’s quantum field theory model

Seminal numerical work by Faddeev and Niemi

Progress reported at Nankai in 2005 with Xiaosong present

Latest unfolding of new results

(Chalk presentation starts from here)

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