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I was surprised that there exist even arithmetic analogies to solitons (more) and Laumon's arithmetic version of an idea of Witten made a new proof of Weil II possible. What else may have arithmetic versions? Ricci flow?

On the Ricci flow-renormalization issue in the comments below, Urs Schreibers answer, an other expert yesterday: "The renormalization that is involved is not the same as in QFT, except for the fact that it can also be thought as realizing, in that geometric context, a subtraction of divergences that has the effect of keeping the flow solutions from blowing up. Whether there is in that context any role for algebraic structures of renormalization, such as Hopf algebras accounting for nested divergences, is a good question."

I was surprised that there exist even arithmetic analogies to solitons (more) and Laumon's arithmetic version of an idea of Witten made a new proof of Weil II possible. What else may have arithmetic versions? Ricci flow?

On the Ricci flow-renormalization issue in the comments below, Urs Schreibers answer, an other expert yesterday: "The renormalization that is involved is not the same as in QFT, except for the fact that it can also be thought as realizing, in that geometric context, a subtraction of divergences that has the effect of keeping the flow solutions from blowing up. Whether there is in that context any role for algebraic structures of renormalization, such as Hopf algebras accounting for nested divergences, is a good question."

I was surprised that there exist even arithmetic analogies to solitons (more) and Laumon's arithmetic version of an idea of Witten made a new proof of Weil II possible. What else may have arithmetic versions? Ricci flow?

I just asked an expert on the Ricci flow-renormalization issue in the comments below: "The renormalization that is involved is not the same as in QFT, except for the fact that it can also be thought as realizing, in that geometric context, a subtraction of divergences that has the effect of keeping the flow solutions from blowing up. Whether there is in that context any role for algebraic structures of renormalization, such as Hopf algebras accounting for nested divergences, is a good question."

I was surprised that there exist even arithmetic analogies to solitons (more) and Laumon's arithmetic version of an idea of Witten made a new proof of Weil II possible. What else may have arithmetic versions? Ricci flow?

On the Ricci flow-renormalization issue in the comments below, Urs Schreibers answer, an other expert yesterday: "The renormalization that is involved is not the same as in QFT, except for the fact that it can also be thought as realizing, in that geometric context, a subtraction of divergences that has the effect of keeping the flow solutions from blowing up. Whether there is in that context any role for algebraic structures of renormalization, such as Hopf algebras accounting for nested divergences, is a good question."

I was surprised that there exist even arithmetic analogies to solitons (more) and Laumon's arithmetic version of an idea of Witten made a new proof of Weil II possible. What else may have arithmetic versions? Ricci flow?

I was surprised that there exist even arithmetic analogies to solitons (more) and Laumon's arithmetic version of an idea of Witten made a new proof of Weil II possible. What else may have arithmetic versions? Ricci flow?

I just asked an expert on the Ricci flow-renormalization issue in the comments below: "The renormalization that is involved is not the same as in QFT, except for the fact that it can also be thought as realizing, in that geometric context, a subtraction of divergences that has the effect of keeping the flow solutions from blowing up. Whether there is in that context any role for algebraic structures of renormalization, such as Hopf algebras accounting for nested divergences, is a good question."