Good afternoon.

Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "classical" data -- the Poisson algebra of functions $C^\infty(M)$ and the cohomology algebra (or rather, Frobenius algebra) $H^\ast(M; \mathbb{C})$ respectively.

Are these two things related somehow? I am interested in both mathematical and physical answers.

I apologize if this question is naive. I feel like, with a proper understanding of the physics, the answer to this question is probably obviously "yes" or obviously "no". Unfortunately, I don't have a good understanding of the physics.

Good afternoon.

Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "classical" data -- the Poisson algebra of functions $C^\infty(M)$ and the cohomology algebra (or rather, Frobenius algebra) $H^\ast(M; \mathbb{C})$ respectively.

Are these two things related somehow?

I am interested in both mathematical and physical answers.

I apologize if this question is naive. I feel like, with a proper understanding of the physics, the answer to this question is probably obviously "yes" or obviously "no". Unfortunately, I don't have a good understanding of the physics.

Edit: From the looks of the discussion below, deformation quantization is perhaps more directly related to the Fukaya category. I welcome any additional remarks on the Fukaya category.

Good afternoon.

Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "classical" data -- the Poisson algebra of functions $C^\infty(M)$ and the cohomology algebra (or rather, Frobenius algebra) $H^\ast(M; \mathbb{C})$ respectively.

Are these two things related somehow? I am interested in both mathematical and physical answers.

Good afternoon.

Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "classical" data -- the Poisson algebra of functions $C^\infty(M)$ and the cohomology algebra (or rather, Frobenius algebra) $H^\ast(M; \mathbb{C})$ respectively.

Are these two things related somehow? I am interested in both mathematical and physical answers.

I apologize if this question is naive. I feel like, with a proper understanding of the physics, the answer to this question is probably obviously "yes" or obviously "no". Unfortunately, I don't have a good understanding of the physics.

Good afternoon.

Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "classical" data -- the Poisson algebra of functions $C^\infty(M)$ and the cohomology algebra (or rather, Frobenius algebra) $H^\ast(M; \mathbb{C})$ respectively.

Are these two things related somehow?

Good afternoon.

Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate respective senses) of "classical" data -- the Poisson algebra of functions $C^\infty(M)$ and the cohomology algebra (or rather, Frobenius algebra) $H^\ast(M; \mathbb{C})$ respectively.

Are these two things related somehow? I am interested in both mathematical and physical answers.