Catalyzes the condensation of two molecules of glyoxylate to give 2-hydroxy-3-oxopropanoate (also termed tartronate semialdehyde). 2 glyoxylate + H(+) = 2-hydroxy-3-oxopropanoate + CO2 Binds 1 Mg(2+) ion per subunit. Binds 1 thiamine pyrophosphate per subunit. Organic acid metabolism; glycolate degradation; 3-phospho-D-glycerate from glycolate: step 2/4. Homotetramer. By glyoxylate. Belongs to the TPP enzyme family.