Here is some information about my academic and industrial achievements.
 
I started very early, as an undergraduate student in FizTech. I am quite proud of my second paper, where we discovered with my best friend Sasha Polyakov dynamical mechanism of symmetry breaking and mass generation in Gauge Theory in 1964, independently of Higgs, Englert and Brout. Conservative Landau School fiercely fought against us, so that our paper got rejected twice in JETP and was finally published only in 1966. Being so delayed we cannot claim credit for this discovery, but we can be satisfied that we stood against retrogrades and fought for the truth we discovered.

Next notable paper was my work with Vladimir Gribov in 1967-68 where we discovered anomalous dimensions in scale invariant field theory. I later applied this, parallel with similar work by Sasha Polyakov- to the critical phenomena in statistical physics.

Our pass was taken by Kenneth Wilson, who scored goal of quantitative theory of phase transitions, applying the renormalization group and his Latex formula expansion.

Still, we had the last word: the conformal bootstrap we discovered was advanced already in this century into quantitative theory by Rychkov. This theory computes both the indexes and correlation functions.

I worked with Gribov for a few years in his Reggeon Field Theory, which was technically quite advanced but became obsolete after discovery of Asymptotic Freedom by Gross, Wilczek and Politzer. I left everything and dove into QCD- The Theory of Strong Interactions.

I discovered quark-resonance duality which led to QCD sum rules of Shifman Wainshtein and Zakharov. I was still working on this theory just two years ago, bringing together the ideas of CFT and String theory, explaining some mysterious relations between my phenomenological QCD spectrum from the 70-ties and remarkable AdS-CFT analogy discovered in the last decades. Remarkably, my phenomenological  formulas, relating the string mass spectrum to the spectrum of dimensions of CFT as roots and indexes of Bessel functions were rediscovered 30 years later in the context of the AdS-CFT duality.

I worked many years in the field of Large N QCD and Quantum Gravity, establishing analogy between QCD and String theory. I have some notable achievements such as Loop Equation in Large N QCD (which reduced field theory to nonlinear 1D problem of loop dynamics).

Another work, which created some excitement in academic community was exact solution of 2D Quantum Gravity, which was started in series of my papers with Volodya Kazakov and was finished with help from David Gross, Edouard Brezin and Shenker and Douglas.

Since that time, in the 90’s my work was mostly some technical advances such as Loop Equations in Turbulence, where  I reduced 3D field theory of decaying turbulence to nonlinear stochastic 1D ODE. This equation can be used to solve large dimension limit of Turbulence (dimension enters as a parameter rather than number of degrees of freedom). Alas, I never finished that work.

Neither did I finish my work on algebraic formulation of the QCD momentum loop equation. Again, it opened the way to exact solution in the infrared limit, which I never found.

Wind of Fate was already blowing and I could not resist its pull. I started new life in the Industry, as an Inventor and Entrepreneur. I opened Internet start-up in mid-90’s with couple of students. A year later I sold the company to the public company and left Academia for good. It was a stressful life, but I never regretted quitting my beloved Princeton University.

Through my academic career I mostly generated ideas, but in my industrial career I had to develop and implement my ideas into working products and technologies. These technologies made it to Windows 98, AOL7, Minolta 3D camera, Lockheed-Martin RealScan3D and other products. I founded a public company and have served as Vice Chairman and Chief Scientist of this company (VWPT) until March 2000, when I left it to work on stock trading system. This is what I did for almost 20 years, with intermittent success, but unwavering enthusiasm.

But the Wind of Fate was not yet finished with me. In 2019 (quite accidentally) I learned that my old friend Katepalli Sreenivasan (Sreeni) finished the large project he started in the 90ties — numerical simulations of Turbulence where he specifically measured the velocity circulation I studied theoretically in 1993 in my Loop Equations.

I predicted the Area Law — the probability distribution for the circulation over the large loop in the turbulent flow depends on the minimal surface bounded by this loop and obeys some universal scaling law.

This prediction went against all the theories (or, more accurately, models) of Turbulence existing in the previous century. So, my theory was shrugged off by experts, as it was shrugged off by them before with the Higgs effect and matrix models of 2D Gravity. Experts went back to their models, and I quit and went to the Industry where you do not need to prove anything as long as your system works.

But Sreeni was persistent: he overcame the objections of the conservative Turbulent community, finished his project, and published his paper. He confirmed my predictions!

The moment I learned that my life changed again. I dropped my financial career — no amount of money can substitute the joy of scientific discovery. Besides, I was never good at making money — it’s one thing to predict the market (which is predictable, to a large extent), and it’s another thing to make a profitable trading system — there are too many business elements there which I have no talent for.

As Pushkin wrote in his “Revival”:

Like this, the darkly apparitions
Are leaving off my tortured heart,
And it again revives the visions
Of virgin days I left behind.

Alexander Pushkin, translated by Yevgeny Bonver

I turned my back to the stock market, applied for the Simons Foundation grant, and got myself a job as a Research Professor at NYU in October 2019. Since then, I have so far published 7 papers in arXiv, and on my 75th birthday, I submitted the 8th paper, summarizing and advancing my new theory.

I had to catch up with Mathematical Physics which evolved during these 25 years I was away. To my big surprise, though, the Turbulence theory was stagnant — everybody was still hypnotized by the Kolmogorov model of 1941.

I had some beginner’s luck, or, better to say, and I had the advantage of a fresh view on the field. The advances made in Gauge Theories for the last 25 years were quite applicable to the Turbulence as well, so I used the analogy of gauge invariance, instantons, and confinement in my new theory.

After inevitable trial and error, I arrived at a novel formulation of the Field Theory of Turbulence (let us cautiously call it a new model), which goes much farther than my Loop Equations. It predicts the shape of circulation distribution, in perfect agreement with the measurements of Sreeni.

There are many more things to do in this new theory, both on the theoretical side and numerical simulations. I am actively collaborating with Sreeni and his postdoc Kartik Iyer.

Harmony and happiness are restored in my life. Like Faustus, I can now say: “Beautiful moment, do not pass away!” Let us just hope that Mephistopheles will not rush to collect his debts from me…

P.S. Now, with more than a dozen papers published on the topic of Turbulence, I may be approaching the final stretch. The theory of vortex surfaces, which I have been developing for many years, is close to completion. Then I may get bored again.

I am not done with the stock market yet! There are some ideas that work in theory, but I could not implement them with the limited resources I had at my own company. These ideas would only work on a global level, with hundreds of thousands of financial instruments traded across all markets. If the Wind of Fate calls me once again, I may not resist a temptation…

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